[User]
Find the number of times the graphs of f(x) = (-1(-5(-1sin(2πx - 2) + 2) + 4) - 2)/(2(-5(-1sin(2πx - 2) + 2) + 4) + 2) and g(x) = 5((-1x + 2)/(1x + 1))^2 + 5((-1x + 2)/(1x + 1)) intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = (-1(-3(-2|x + 1| + 2)^2 + 1(-2|x + 1| + 2) + 1) + 3)/(-1(-3(-2|x + 1| + 2)^2 + 1(-2|x + 1| + 2) + 1) + 2) and g(x) = (3(3cos(2πx - 2) - 1) - 2)/(3(3cos(2πx - 2) - 1) + 2) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 1(-1|(2e^(-1x) - 2) + 2| + 2)^2 + 2(-1|(2e^(-1x) - 2) + 2| + 2) + 4 and g(x) = 2cos(2π((-1x)/(-3x - 2)) + 3) + 2 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 3cos(1π(-5(-3x + 1)^2 + 2(-3x + 1) - 3) - 3) - 1 and g(x) = 3(1|x - 2| - 3) - 3 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 1(-1(-2|x + 3| - 2) - 4)^2 - 5(-1(-2|x + 3| - 2) - 4) + 2 and g(x) = -2cos(1π(-2x + 3) - 1) + 3 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -3e^(2(-2|(-4x - 2) - 3| + 2)) + 2 and g(x) = (2(-3x^2 - 1x + 2) + 3)/(-3(-3x^2 - 1x + 2) - 2) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = (2((1(-2|x - 3| + 1) - 1)/(-2(-2|x - 3| + 1))) - 3)/(3((1(-2|x - 3| + 1) - 1)/(-2(-2|x - 3| + 1))) + 1) and g(x) = 1(3cos(3πx - 1))^2 - 1(3cos(3πx - 1)) + 1 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation (-2(1sin(3π(-5x + 5) - 3) + 2) + 3)/(1(1sin(3π(-5x + 5) - 3) + 2)) = -3sin(3π((-3x - 1)/(-1x - 3)) - 2) - 3 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 2sin(2π(2|(-4x^2 + 4x + 5) - 2| - 1) + 2) and g(x) = -3(3cos(3πx - 1) - 2) + 2 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 1(-2e^(-2(2x^2 - 3x + 3)))^2 - 3(-2e^(-2(2x^2 - 3x + 3))) - 2 and g(x) = -2|(3sin(3πx - 2) - 2) + 2| + 1 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation (1(-2cos(3π((2x + 2)/(2x - 1)) + 3)) - 2)/(-3(-2cos(3π((2x + 2)/(2x - 1)) + 3)) - 2) = -1sin(3π(-1|x + 3| + 1) - 1) - 2 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 2cos(1π(2|(2x + 3) - 2| - 3)) + 1 and g(x) = 1e^(1((-3x - 2)/(3x + 2))) - 1 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation (3(-3(2|x + 1| - 1)^2 + 3(2|x + 1| - 1) + 4) + 1)/(-2(-3(2|x + 1| - 1)^2 + 3(2|x + 1| - 1) + 4)) = -1e^(-1(1x^2 + 1)) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -3|(-1(1x^2 + 2) + 4)| - 2 and g(x) = -1|((-3x - 2)/(-1x - 2))| - 3 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = (1((-1((2x + 1)/(1x - 3)) - 3)/(1((2x + 1)/(1x - 3)) - 2)) - 2)/(3((-1((2x + 1)/(1x - 3)) - 3)/(1((2x + 1)/(1x - 3)) - 2)) - 2) and g(x) = -3cos(2π((2x + 1)/(3x - 2)) + 2) - 2 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = (-2(-3sin(3π(2|x - 1| - 3) - 2) + 2) - 2)/(-1(-3sin(3π(2|x - 1| - 3) - 2) + 2) + 2) and g(x) = -3|(-3cos(3πx - 3) - 3) - 2| - 3 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 2sin(2π(2(5x^2 - 4x + 1)^2 + 5(5x^2 - 4x + 1) + 3) - 3) and g(x) = (-2((-2x - 1)/(-2x - 2)) - 2)/(2((-2x - 1)/(-2x - 2))) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -3|((-2(2|x + 2| + 1) + 2)/(-1(2|x + 2| + 1) + 2)) - 1| = (1(3cos(1πx - 3) - 2) - 3)/(-1(3cos(1πx - 3) - 2)) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -1cos(2π(3(-2|x - 2| + 1)^2 - 3(-2|x - 2| + 1) - 4) + 1) + 2 and g(x) = 2sin(3π((-1x + 2)/(-3x + 1)) - 1) - 1 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -2(-1(1sin(2πx - 2))^2 + 3(1sin(2πx - 2)) - 2) - 2 and g(x) = (1((2x + 1)/(-2x + 3)) - 2)/(2((2x + 1)/(-2x + 3)) + 1) where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -1((3(-2x^2 + 1x - 5) - 1)/(2(-2x^2 + 1x - 5) + 2)) + 4 = 1|(4x^2 - 3x - 5) + 1| have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -3sin(3π(-1|(-1x + 4) - 3| + 3) - 2) - 1 and g(x) = -1e^(1(-4x^2 - 4x)) - 3 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 5((1(1|x + 3| - 2) + 2)/(1(1|x + 3| - 2) + 1))^2 - 5((1(1|x + 3| - 2) + 2)/(1(1|x + 3| - 2) + 1)) - 1 and g(x) = (-1(-5x^2 - 1x - 5) - 2)/(-3(-5x^2 - 1x - 5) - 1) where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = (1(4(-2x - 2) + 5) + 3)/(3(4(-2x - 2) + 5) + 1) and g(x) = 2cos(1π(1x + 1) - 3) where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -2cos(2π(-3(-4x - 5)^2 - 1(-4x - 5) - 3) + 2) - 1 and g(x) = (-1(5x - 5) + 2)/(2(5x - 5)) where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -2(1cos(1π(-3x^2 - 3x - 4) + 3) - 1)^2 + 4(1cos(1π(-3x^2 - 3x - 4) + 3) - 1) - 5 and g(x) = -2|(1x^2 + 2x + 5)| - 3 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = (-3(2|((-3x - 1)/(-3x + 2)) + 3| - 3))/(2(2|((-3x - 1)/(-3x + 2)) + 3| - 3) + 3) and g(x) = -3cos(1π(-5x + 3)) - 1 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 3(-3(-3cos(2πx + 3) - 1) - 3) + 5 and g(x) = (-1(1cos(3πx - 2) + 3) + 1)/(1(1cos(3πx - 2) + 3) - 3) intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -3|(1(2|x + 2|)^2 + 1(2|x + 2|) - 1) - 1| + 3 = (-1(2e^(2x) - 3) - 3)/(-3(2e^(2x) - 3) + 2) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -3cos(1π(4(1x + 3)^2 - 2(1x + 3) + 4) + 1) + 3 and g(x) = 2(-1x^2 + 3x + 3)^2 - 4(-1x^2 + 3x + 3) + 5 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -5(5(-3|x + 3| + 3))^2 - 5(5(-3|x + 3| + 3)) + 4 and g(x) = (1(1cos(3πx + 2) - 2))/(1(1cos(3πx + 2) - 2) + 3) where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 3|(2(-3cos(3πx + 3) - 1) - 4) - 2| + 3 and g(x) = 1(1x^2 + 5x + 4) + 5 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -2((-2(-1sin(3πx + 3) - 3) + 3)/(-2(-1sin(3πx + 3) - 3) - 1)) + 3 and g(x) = 5(3cos(1πx + 2) - 1) - 3 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -3(-1cos(1π(1x - 1) + 3) + 2) + 3 = -2e^(1(-4x^2 - 2x - 1)) - 1 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = (2(2|(-2cos(1πx - 3) + 2) - 3| - 2) + 1)/(2(2|(-2cos(1πx - 3) + 2) - 3| - 2) - 3) and g(x) = -3cos(3π(-1|x - 2| + 1)) + 1 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 3|(-1e^(1(-2|x - 3| - 1)))| - 3 = -2cos(2π((1x + 1)/(2x)) + 2) - 1 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -3cos(1π(-5(-1|x + 1| - 1)^2 - 5(-1|x + 1| - 1) - 3) + 3) + 2 = (1(1|x| + 1) - 3)/(-2(1|x| + 1) + 3) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = (-3(2|(1|x + 1| + 1) - 3|) - 2)/(2(2|(1|x + 1| + 1) - 3|) + 3) and g(x) = 2cos(3π(4x^2 - 2x - 1) - 1) - 1 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 2(-2sin(3π(-5x - 4) + 2) - 2)^2 - 3(-2sin(3π(-5x - 4) + 2) - 2) - 4 and g(x) = -3cos(1π((-2x - 2)/(-1x)) + 1) - 1 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -2sin(1π(-3(3x^2 + 5x + 3)^2 - 2) + 3) + 1 and g(x) = 3e^(1((3x + 2)/(-2x + 3))) - 2 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -3|(-2sin(3π(5x + 2)) + 1)| + 2 and g(x) = -3|(2|x + 2| - 3) + 3| - 1 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 3(-3cos(2π((3x - 3)/(-2x)) - 2) - 1)^2 - 5 = -5(-2|x + 2|) + 3 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -1(3sin(3π(4x - 1) - 1) - 1) and g(x) = 1|(-3x + 4) + 1| in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -2|((-1(-1x + 1))/(-1(-1x + 1) + 2)) + 3| - 1 = 5(-2sin(3πx - 1) - 2)^2 + 5(-2sin(3πx - 1) - 2) - 4 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -2(2sin(3π(-1|x - 2| + 3) - 1))^2 - 4(2sin(3π(-1|x - 2| + 3) - 1)) + 1 and g(x) = 3sin(2π(1|x| - 1)) + 3 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -3cos(2π((3(2x^2 - 2) + 2)/(2(2x^2 - 2) - 1)) - 2) + 3 = -3cos(2π(3|x - 3| - 2) + 1) + 3 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -2(2cos(3π((-1x + 2)/(3x - 2)) - 3) - 3) - 2 = 2((2x - 3)/(-1x - 3))^2 + 5((2x - 3)/(-1x - 3)) - 2 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -5((2(-2cos(3πx + 1) + 1) - 3)/(-2(-2cos(3πx + 1) + 1)))^2 - 1 and g(x) = (-3(-3cos(3πx + 2) + 1) + 1)/(3(-3cos(3πx + 2) + 1) - 2) where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 1e^(-1(1(5x^2 - 2x))) + 2 and g(x) = 2sin(2π(-2x + 2) + 1) + 2 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -2|(-5(-1|x + 2| - 1)^2 + 4(-1|x + 2| - 1)) - 3| + 3 and g(x) = -2(2x^2 + 5x - 5)^2 + 4(2x^2 + 5x - 5) + 1 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 1((3((-2x)/(2x + 3)) + 2)/(-3((-2x)/(2x + 3)) + 4))^2 + 4((3((-2x)/(2x + 3)) + 2)/(-3((-2x)/(2x + 3)) + 4)) - 5 and g(x) = -2(-3cos(1πx - 3) + 3)^2 + 3(-3cos(1πx - 3) + 3) - 1 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -1((2(3cos(2πx)) - 1)/(-3(3cos(2πx)) + 2))^2 + 3((2(3cos(2πx)) - 1)/(-3(3cos(2πx)) + 2)) + 3 and g(x) = (1(5x^2 - 4x + 1) - 1)/(1(5x^2 - 4x + 1) + 2) intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 1cos(3π(-1|(2x + 3) - 2| - 3) + 1) + 1 = 3|(-1x + 2) - 3| - 1 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = (1(2|(-1|x - 3| + 1) + 1| - 2) - 1)/(3(2|(-1|x - 3| + 1) + 1| - 2) - 2) and g(x) = (3(3|x + 1| + 3) - 3)/(3(3|x + 1| + 3) + 3) intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = (3(-3sin(3π(1x + 1) + 2) + 2) - 3)/(3(-3sin(3π(1x + 1) + 2) + 2) - 2) and g(x) = (2(-5x + 4) - 3)/(-3(-5x + 4) - 3) intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -2cos(2π(3(-3|x + 2| - 3) + 1)) - 1 and g(x) = -4(-2x^2 + 3x + 4) - 1 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 1(3(3|x + 1| - 3)^2 + 5(3|x + 1| - 3) + 1)^2 - 1(3(3|x + 1| - 3)^2 + 5(3|x + 1| - 3) + 1) + 2 and g(x) = -2(-3|x + 2| - 3) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 3sin(2π(-2|(3x) + 1|) + 1) + 3 and g(x) = 3cos(3π(4x + 3) - 1) + 2 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = (1(-5(-1cos(3πx + 3) + 1) + 4) - 1)/(2(-5(-1cos(3πx + 3) + 1) + 4) + 2) and g(x) = (3(-1sin(2πx + 3) + 1) + 3)/(-3(-1sin(2πx + 3) + 1)) where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -3(3|(-1x^2 - 3x + 4) + 2| - 1)^2 - 4(3|(-1x^2 - 3x + 4) + 2| - 1) + 4 and g(x) = -5(2|x - 3| - 2)^2 + 4(2|x - 3| - 2) - 4 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 4(2|(1x^2 - 4x + 3) + 2| + 1) - 4 and g(x) = (-1(-1cos(1πx - 3)) + 2)/(-3(-1cos(1πx - 3)) + 1) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -3cos(1π(4(2|x| + 2) - 4) + 3) + 3 and g(x) = 1|(-2sin(3πx - 3)) + 2| intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -2(2|(4x + 2) + 2| - 1)^2 + 3(2|(4x + 2) + 2| - 1) + 2 and g(x) = (2(-3sin(2πx - 1) - 2) + 3)/(-3(-3sin(2πx - 1) - 2) - 1) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 2|(5(-1x - 4) + 3) - 1| + 1 = 1|((1x - 2)/(-3x - 3)) - 2| + 3 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -5(-3(-2x + 4) + 1)^2 + 4(-3(-2x + 4) + 1) + 1 = -3((2x + 3)/(-1x))^2 - 5((2x + 3)/(-1x)) + 5 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation (2(4(1cos(3πx - 3) - 3) - 3) + 1)/(3(4(1cos(3πx - 3) - 3) - 3) - 1) = -2|(2|x - 2| + 2) - 3| + 1 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -5(1cos(2π(1|x + 1|) + 2)) + 2 and g(x) = 2|(-3cos(3πx + 3) + 1) - 1| - 3 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation (-2(-2(2cos(3πx - 1) + 2)^2 + 5(2cos(3πx - 1) + 2) - 1) + 3)/(2(-2(2cos(3πx - 1) + 2)^2 + 5(2cos(3πx - 1) + 2) - 1) + 2) = 2|((-1x + 3)/(-1x - 2)) + 3| + 3 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation (-2(-2cos(2π(-1x^2 - 4x) + 1)) - 3)/(2(-2cos(2π(-1x^2 - 4x) + 1)) - 3) = (3(2sin(2πx)) - 2)/(3(2sin(2πx)) - 1) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -5(3cos(1π(2|x - 3| - 3)) + 2)^2 + 1(3cos(1π(2|x - 3| - 3)) + 2) + 2 = 3((2x + 2)/(1x - 2)) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 4(3cos(1π(-4x^2 + 4) + 2) + 1)^2 + 1(3cos(1π(-4x^2 + 4) + 2) + 1) + 2 = 1(-1|x + 2| + 3)^2 + 2(-1|x + 2| + 3) - 2 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 3sin(1π(1(4x^2 - 2x + 2)^2 + 3(4x^2 - 2x + 2) - 1) + 1) + 3 and g(x) = (2(-4x^2 - 1x + 1) - 2)/(-2(-4x^2 - 1x + 1) - 3) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 1(-1sin(2π(1x^2 - 1x + 5) - 1) + 1) + 2 = 1(1|x - 1| - 3) - 5 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = (2(1e^(-2(1|x - 3| + 3)) + 1) + 2)/(3(1e^(-2(1|x - 3| + 3)) + 1)) and g(x) = (-3(-2sin(2πx + 3) + 2) + 2)/(1(-2sin(2πx + 3) + 2)) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation (-2(-1((-1x + 3)/(2x + 2)) - 5) + 2)/(-3(-1((-1x + 3)/(2x + 2)) - 5) - 1) = -2sin(1π(3x - 2) + 1) - 1 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 5((3(-3cos(3πx) + 3))/(2(-3cos(3πx) + 3) + 3))^2 + 1((3(-3cos(3πx) + 3))/(2(-3cos(3πx) + 3) + 3)) - 5 and g(x) = 3|(-2cos(2πx - 1) + 2) - 2| + 1 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation (3((-2(3sin(1πx - 3) - 2) - 2)/(-1(3sin(1πx - 3) - 2) + 2)))/(2((-2(3sin(1πx - 3) - 2) - 2)/(-1(3sin(1πx - 3) - 2) + 2)) + 3) = -3|(2x^2 - 1x) - 3| - 3 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -4(2(4x - 1)^2 + 1(4x - 1) - 4) - 4 = (2(1cos(2πx - 1) - 1) + 2)/(-1(1cos(2πx - 1) - 1)) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -3(1(1x^2 - 5x + 1)^2 + 4(1x^2 - 5x + 1) + 4)^2 + 5(1(1x^2 - 5x + 1)^2 + 4(1x^2 - 5x + 1) + 4) + 1 and g(x) = -3sin(3π(1x^2 + 3x + 2) + 3) + 3 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = (-3(-2(-3|x| + 3)) - 2)/(1(-2(-3|x| + 3)) + 1) and g(x) = 1(-3x^2 + 5x - 5) + 3 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 3|(-2((-2x - 2)/(2x + 3)) - 5) + 2| - 2 and g(x) = -3|(-2cos(2πx + 3) + 2) - 3| + 3 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -2(3(1cos(3πx - 1) - 1)^2 + 2(1cos(3πx - 1) - 1))^2 - 4(3(1cos(3πx - 1) - 1)^2 + 2(1cos(3πx - 1) - 1)) - 4 and g(x) = 1cos(1π(1x^2 - 1x - 3) - 1) - 2 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = (1(-5(-1|x + 1| + 3) + 2) + 3)/(2(-5(-1|x + 1| + 3) + 2) + 1) and g(x) = 2|((2x - 2)/(-3x - 2)) - 1| - 2 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 1sin(3π(1((-3x - 3)/(1x + 2))^2 + 1((-3x - 3)/(1x + 2)) - 2) + 2) - 2 = -2(-2|x - 1|) - 4 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = (-1((3(3cos(2πx - 2) + 1) - 3)/(2(3cos(2πx - 2) + 1) - 1)) - 3)/(-2((3(3cos(2πx - 2) + 1) - 3)/(2(3cos(2πx - 2) + 1) - 1)) - 2) and g(x) = -3sin(2π(2x - 5) - 3) + 2 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation (-2(-1(5x^2 - 4x - 5)^2 + 1(5x^2 - 4x - 5) + 1) + 3)/(1(-1(5x^2 - 4x - 5)^2 + 1(5x^2 - 4x - 5) + 1) + 2) = 1|(-2sin(2πx + 2) + 2)| - 1 have for x in the interval [-10, 10]?

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[User]
How many points of intersection exist between the functions f(x) = -2sin(1π(1(-3|x| + 1)^2 + 3(-3|x| + 1) - 2) + 1) - 1 and g(x) = (-2(-2x^2 + 3x - 2))/(-3(-2x^2 + 3x - 2) + 4) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -1|((-2(-3|x + 1| + 1) - 3)/(3(-3|x + 1| + 1))) - 3| and g(x) = (-1(3|x + 1| - 2) + 1)/(3(3|x + 1| - 2)) intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 1|(4(-3x)^2 - 4(-3x) + 3) + 2| + 2 and g(x) = (2(2sin(3πx + 3)))/(-2(2sin(3πx + 3)) + 3) where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = (-2(4(-3x^2 - 1)^2 - 3(-3x^2 - 1) - 5))/(3(4(-3x^2 - 1)^2 - 3(-3x^2 - 1) - 5) + 1) and g(x) = -3sin(3π(-1x^2 + 5x - 5) - 1) - 2 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -4(3sin(1π(2x - 3)) - 1) - 1 and g(x) = -5(1x + 4)^2 - 5(1x + 4) + 5 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = (2(-2sin(2π((-2x - 2)/(-3x)) - 1) - 2) + 3)/(2(-2sin(2π((-2x - 2)/(-3x)) - 1) - 2) - 1) and g(x) = -3sin(1π(1x - 1) - 2) - 1 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation (3(3|(1x^2 + 3)| - 3) + 1)/(-1(3|(1x^2 + 3)| - 3) + 2) = 3cos(3π(-3x + 5) + 2) - 1 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 4(-2(-3sin(2πx + 2) + 2) - 1)^2 - 1(-2(-3sin(2πx + 2) + 2) - 1) - 4 and g(x) = 1(1x) - 4 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -1|(1(-4x^2 + 3x + 5)^2 + 4(-4x^2 + 3x + 5) - 5) - 2| - 3 and g(x) = -5((-1x)/(-1x + 2)) - 5 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 1e^(-1((-1(-5x - 3) + 1)/(3(-5x - 3) - 1))) - 2 and g(x) = -2(-1|x + 3| + 2)^2 - 4(-1|x + 3| + 2) + 1 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = (-1(-1((3x)/(-3x - 1)) + 3) - 3)/(3(-1((3x)/(-3x - 1)) + 3) - 2) and g(x) = 3cos(2π(-3x) - 1) - 1 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -2(2cos(3π((1x + 2)/(2x - 3)) + 1) + 1)^2 + 4(2cos(3π((1x + 2)/(2x - 3)) + 1) + 1) + 2 = 3(-2x + 3)^2 + 2(-2x + 3) - 3 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -2((3(-2|x + 3| - 2) + 3)/(3(-2|x + 3| - 2) - 1))^2 + 3((3(-2|x + 3| - 2) + 3)/(3(-2|x + 3| - 2) - 1)) - 2 = -2sin(2π(4x^2 - 4x - 1) - 2) + 1 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -1|(5(-3sin(2πx + 1) + 1)^2 + 1(-3sin(2πx + 1) + 1))| + 3 and g(x) = -1|(3x + 4) + 1| - 3 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 1(-2((-1x + 3)/(-3x + 1))^2 + 5((-1x + 3)/(-3x + 1)) + 4)^2 - 5(-2((-1x + 3)/(-3x + 1))^2 + 5((-1x + 3)/(-3x + 1)) + 4) + 1 and g(x) = 2|(-2sin(3πx + 1) + 3) + 3| + 3 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -3(-3sin(3π(-1|x + 3| - 1) + 2) - 2)^2 + 5 and g(x) = -3cos(3π(-1x^2 - 1x + 2) - 1) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -5((3(-2|x + 1| + 2) + 1)/(-1(-2|x + 1| + 2) - 3)) - 2 and g(x) = 2(3cos(2πx - 1) - 1) - 3 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 3e^(1(1|((1x - 3)/(2x - 1)) + 3| - 2)) - 1 = 3|(-3sin(1πx - 2)) - 3| have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 3(2sin(1π((-1x)/(-1x - 3)) - 3) - 3)^2 + 4(2sin(1π((-1x)/(-1x - 3)) - 3) - 3) + 1 and g(x) = 1((-2x - 2)/(-1x - 2)) - 5 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = (1((1(-1x^2 + 2x - 1))/(1(-1x^2 + 2x - 1) + 1)) + 1)/(-1((1(-1x^2 + 2x - 1))/(1(-1x^2 + 2x - 1) + 1)) + 2) and g(x) = 3cos(1π(5x^2 - 2x + 1) - 3) - 3 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 1(-1sin(2π(-3x - 4) - 1) - 3)^2 + 4(-1sin(2π(-3x - 4) - 1) - 3) + 1 and g(x) = (2((-2x - 2)/(-2x + 3)) + 1)/(-1((-2x - 2)/(-2x + 3)) + 2) where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 4((3(-2x^2 + 3x - 1) - 1)/(3(-2x^2 + 3x - 1) + 2)) + 5 and g(x) = -3sin(3π(-2x - 5) + 2) + 1 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 3((-3(3e^(2x) + 1) + 3)/(2(3e^(2x) + 1) + 2))^2 + 1((-3(3e^(2x) + 1) + 3)/(2(3e^(2x) + 1) + 2)) + 2 and g(x) = -1sin(3π(-4x - 5) - 1) + 1 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 1((3(1|x - 2|) - 1)/(-3(1|x - 2|))) - 4 and g(x) = -3sin(3π((-2x)/(-1x + 3)) + 2) intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 3(3(-2x^2 + 5x + 1) + 1)^2 - 4(3(-2x^2 + 5x + 1) + 1) - 4 and g(x) = -1cos(1π(-2|x + 3|) + 1) + 2 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = (-1(-1sin(2π(-3x^2 - 5x - 1) - 2) - 3) + 2)/(2(-1sin(2π(-3x^2 - 5x - 1) - 2) - 3) + 2) and g(x) = -3sin(3π((-2x - 1)/(1x)) + 3) - 3 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = (2(1cos(1π(-5x^2 + 3x - 3) + 2) - 1) + 1)/(-2(1cos(1π(-5x^2 + 3x - 3) + 2) - 1) + 1) and g(x) = -4((3x + 3)/(-2x + 3)) - 5 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 1sin(2π(-1|(-2x + 1) - 3| - 1) - 2) - 2 = 1cos(2π(-5x - 4) + 3) - 3 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = (3(-2|(3|x - 2| - 1)| - 1) - 2)/(1(-2|(3|x - 2| - 1)| - 1) - 3) and g(x) = 3|(3|x - 1| - 3) - 1| - 3 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -1(1|(-5x^2 - 5x + 5) + 1| - 1)^2 - 4(1|(-5x^2 - 5x + 5) + 1| - 1) and g(x) = 3|(-1cos(1πx + 1)) - 2| - 2 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 3e^(2(-3|(5x + 3) + 1| + 1)) - 2 = (-1(2|x + 1| - 2) - 1)/(2(2|x + 1| - 2) - 3) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = (-3((-3(-1x^2 + 4x) + 3)/(-3(-1x^2 + 4x) - 3)) - 1)/(3((-3(-1x^2 + 4x) + 3)/(-3(-1x^2 + 4x) - 3)) - 2) and g(x) = (3(3x^2 + 5x + 1) - 2)/(2(3x^2 + 5x + 1) + 2) intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = (3(1sin(3π(3x^2 + 4x)) - 3) + 3)/(-3(1sin(3π(3x^2 + 4x)) - 3) - 1) and g(x) = 2sin(1π(-2x - 2) - 3) + 1 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 2|(-3(2|x - 2| - 3)^2 + 5(2|x - 2| - 3) + 3) - 1| + 1 and g(x) = (-3(-1sin(2πx - 3) + 2) + 2)/(-2(-1sin(2πx - 3) + 2) + 3) where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 2sin(2π((-1(-1|x + 2| - 2) - 1)/(2(-1|x + 2| - 2) + 2)) + 3) - 3 and g(x) = -5(-3x^2 - 1x + 4)^2 - 2(-3x^2 - 1x + 4) - 3 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -1cos(2π(-2|(-1x - 4)| - 1) + 1) - 1 and g(x) = (1(-4x^2 - 3x - 4) + 1)/(-2(-4x^2 - 3x - 4) + 3) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -4(-3cos(2π(3|x| - 1) + 2))^2 - 3(-3cos(2π(3|x| - 1) + 2)) - 3 = -3e^(1(2|x - 2| + 2)) - 1 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 4(1((-2x + 2)/(-3x - 1))^2) and g(x) = -5(-2sin(3πx - 1)) + 2 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -2e^(2((3((1x + 2)/(2x + 3)) - 3)/(2((1x + 2)/(2x + 3)) + 1))) and g(x) = -3sin(2π(3|x + 1| - 2) - 3) - 2 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -1(-2|((-2x)/(1x + 1)) + 3| - 2) - 3 and g(x) = (-1(-1|x - 2| + 2) - 3)/(3(-1|x - 2| + 2)) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 3cos(3π(2((-1x + 2)/(-1x + 2))^2 - 3((-1x + 2)/(-1x + 2)) + 5) - 2) + 2 and g(x) = 1sin(2π(-5x^2 + 5x - 3) - 1) + 1 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = (-1(3sin(3π(1|x + 3| - 1) - 2)) - 3)/(3(3sin(3π(1|x + 3| - 1) - 2)) + 3) and g(x) = 2((-2x - 2)/(-1x + 3))^2 + 1((-2x - 2)/(-1x + 3)) + 1 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 3cos(1π(1|(2x - 4) - 2|) - 3) - 1 and g(x) = (-3((-1x)/(-1x + 2)) + 3)/(-1((-1x)/(-1x + 2)) - 1) intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 3|(-3cos(1π(1|x - 1| - 3) + 3) - 1) - 1| - 1 and g(x) = 5(1|x + 2|) where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = (-1(2(3cos(3πx + 2) - 1) - 2))/(-2(2(3cos(3πx + 2) - 1) - 2) - 2) and g(x) = -5(2cos(3πx + 3) - 3)^2 - 1(2cos(3πx + 3) - 3) intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = (-2(1(1x^2 + 5x - 1)^2 + 5(1x^2 + 5x - 1) + 2) + 1)/(1(1(1x^2 + 5x - 1)^2 + 5(1x^2 + 5x - 1) + 2)) and g(x) = 2|(1cos(3πx - 1) + 2)| intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 1|(2sin(1π(4x - 4) - 1) + 1) + 1| - 1 = (3(-5x^2 - 5x + 5))/(-2(-5x^2 - 5x + 5) - 2) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -3|(2e^(2(2|x + 3| - 2))) - 3| + 3 and g(x) = (-2(3x - 2) - 1)/(-2(3x - 2) - 1) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -5(-1(-1x - 1)^2 - 5(-1x - 1) - 2) + 5 and g(x) = (-2(3cos(3πx - 1)) - 3)/(1(3cos(3πx - 1)) + 2) intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -4(-2|(1|x + 1| - 3) - 3| + 2) + 3 and g(x) = -1cos(3π(1x + 4) + 1) - 3 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -2sin(3π(-3|(-5x^2 - 3x + 4) - 2| + 2) - 3) - 2 and g(x) = (-2(1sin(2πx + 1) - 3) + 1)/(1(1sin(2πx + 1) - 3) + 1) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -5(3sin(3π(-2|x - 3|)))^2 - 1(3sin(3π(-2|x - 3|))) - 4 and g(x) = -2(-5x + 5) + 3 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = (1(1(3sin(2πx - 3) - 3) + 1) + 3)/(3(1(3sin(2πx - 3) - 3) + 1)) and g(x) = -2((3x + 2)/(-2x + 3))^2 - 2((3x + 2)/(-2x + 3)) + 2 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -2cos(2π(3|(3x - 5) + 3| + 1) + 2) - 3 and g(x) = -2|(-2x - 3) + 1| - 2 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = (-1(1|(5x) + 1| + 2) - 1)/(-1(1|(5x) + 1| + 2) + 3) and g(x) = 3sin(1π(4x + 1) - 2) - 1 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = (-1(2e^(-2(1x^2 - 4x - 4)) - 3))/(-3(2e^(-2(1x^2 - 4x - 4)) - 3) + 4) and g(x) = -2cos(2π(-3|x - 1| + 1) + 2) + 2 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 4(-1|((-3x + 3)/(1x - 2)) + 3| + 3)^2 + 4(-1|((-3x + 3)/(1x - 2)) + 3| + 3) - 4 = (-2((-3x + 1)/(-3x - 3)))/(3((-3x + 1)/(-3x - 3)) + 2) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 1((1(-1x - 1) + 2)/(2(-1x - 1) + 1))^2 - 3((1(-1x - 1) + 2)/(2(-1x - 1) + 1)) - 4 and g(x) = (1(3|x| - 2) - 2)/(1(3|x| - 2) - 3) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 5(-4(2sin(3πx + 1)) + 5) - 5 = -3(-3sin(2πx + 1) - 3)^2 + 5(-3sin(2πx + 1) - 3) + 4 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = (-2(-5(-3x^2 - 5x + 2)^2 + 4(-3x^2 - 5x + 2) + 3) - 1)/(1(-5(-3x^2 - 5x + 2)^2 + 4(-3x^2 - 5x + 2) + 3)) and g(x) = 1(1e^(2x))^2 + 5(1e^(2x)) - 3 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = (-3(-2(-1x^2 + 2) - 2) + 1)/(2(-2(-1x^2 + 2) - 2) + 3) and g(x) = -2(3cos(1πx + 2)) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -1sin(3π((-1(1x^2 - 2x - 2) - 2)/(-2(1x^2 - 2x - 2) + 1))) - 2 and g(x) = -2cos(2π((3x + 3)/(3x + 3)) + 2) - 2 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = (2((2(2cos(3πx + 1)) + 2)/(3(2cos(3πx + 1)) - 2)) - 2)/(-1((2(2cos(3πx + 1)) + 2)/(3(2cos(3πx + 1)) - 2))) and g(x) = 1|((-3x + 3)/(-1x + 3)) - 1| + 2 where -10 ≤ x ≤ 10.

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[User]
Find the number of times the graphs of f(x) = (-3(2((-2x - 3)/(-2x + 1)) - 2) - 3)/(-2(2((-2x - 3)/(-2x + 1)) - 2) + 3) and g(x) = 2sin(2π((2x + 3)/(-1x)) - 2) + 2 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 2|(-3(5x^2 + 2x - 2) - 3) + 2| - 1 and g(x) = 1((1x - 2)/(1x - 3)) + 5 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 1(-3sin(2π(-5x + 4) + 1) + 1)^2 + 1(-3sin(2π(-5x + 4) + 1) + 1) - 5 and g(x) = (-1(-3x + 1) - 1)/(3(-3x + 1)) intersect in the interval [-10, 10].

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[User]
How many solutions does the equation 2sin(2π((1((-3x + 3)/(-2x + 3)) + 3)/(2((-3x + 3)/(-2x + 3)))) - 1) + 1 = (-3(5x^2 + 4x + 5) - 3)/(3(5x^2 + 4x + 5) + 3) have for x in the interval [-10, 10]?

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[User]
How many solutions does the equation 2|(3cos(3π((-2x - 2)/(-1x - 2))) + 2) - 2| = -3sin(1π((1x - 1)/(-1x + 2)) - 2) + 1 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 1((-2(-4x^2 - 5x - 4) + 3)/(-1(-4x^2 - 5x - 4) + 3)) - 4 and g(x) = 3cos(1π(1x + 5) + 1) - 1 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -1(-3(1cos(3πx - 1)) + 2) + 3 and g(x) = (-1(-3cos(1πx + 2) - 2) + 2)/(-3(-3cos(1πx + 2) - 2) + 2) intersect in the interval [-10, 10].

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[User]
How many points of intersection exist between the functions f(x) = -2sin(1π(-3|(1x^2 + 4x - 3)| + 3) - 3) + 3 and g(x) = (2(1|x| + 1) + 2)/(1(1|x| + 1) + 2) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -1cos(2π(3(1|x - 3| - 3) - 5) + 2) + 3 and g(x) = 2|(1|x - 2| - 3) - 1| in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = (2(-3|(-2cos(3πx + 2))| - 1) + 2)/(1(-3|(-2cos(3πx + 2))| - 1) + 1) and g(x) = 1(-2sin(3πx + 3))^2 - 4(-2sin(3πx + 3)) - 4 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation (-2(2|(-2e^(-1x) - 1) + 2| - 2) - 2)/(2(2|(-2e^(-1x) - 1) + 2| - 2) + 2) = 2sin(1π((-2x + 1)/(-1x - 1)) + 2) - 3 have for x in the interval [-10, 10]?

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[User]
How many solutions does the equation 3cos(1π(-1|(3x - 2) - 2| + 3) + 2) + 3 = -2|(1|x - 3| + 1) - 2| + 3 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -2sin(2π(-2|(1x + 3) + 2| - 3) + 1) + 1 and g(x) = 2e^(2((2x - 3)/(-3x + 4))) intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -1sin(2π(-2|(-3x^2 - 3x - 3) - 3| + 1) + 1) - 3 and g(x) = -4((-1x)/(-2x + 3)) - 1 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 2(2|(-1x + 2) + 1| - 3)^2 - 5(2|(-1x + 2) + 1| - 3) - 2 and g(x) = 5((1x)/(-3x - 3)) + 2 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -3(3sin(3π(-4x - 3) + 2) + 1) - 4 and g(x) = 2(3e^(2x) - 2)^2 + 3(3e^(2x) - 2) - 1 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -1|((-1(-1x^2 - 4x + 2) + 1)/(-3(-1x^2 - 4x + 2) + 1)) + 2| + 3 and g(x) = 2(-2e^(1x) + 3)^2 - 3(-2e^(1x) + 3) - 2 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -5(1|((3x - 3)/(-1x + 2)) + 3| - 3)^2 + 3(1|((3x - 3)/(-1x + 2)) + 3| - 3) + 1 and g(x) = -5(3cos(2πx + 2) + 1)^2 - 1(3cos(2πx + 2) + 1) + 5 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -1cos(3π(5(-1x - 2)^2 - 3(-1x - 2) - 5) + 3) = (1(-1x))/(-3(-1x) + 2) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = (-3(2(1|x + 2| - 2)^2 + 2(1|x + 2| - 2) - 5) - 3)/(2(2(1|x + 2| - 2)^2 + 2(1|x + 2| - 2) - 5) - 1) and g(x) = (-1(3|x| + 2) + 2)/(3(3|x| + 2) - 2) where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -1|(1((-2x + 3)/(3x - 2))^2 - 4((-2x + 3)/(3x - 2)) - 1) + 2| - 1 = 3(-1|x - 2|)^2 + 4(-1|x - 2|) - 2 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -1(2cos(2π(3|x - 1| + 2)) + 1)^2 + 3(2cos(2π(3|x - 1| + 2)) + 1) - 2 and g(x) = (1(1sin(2πx) - 2) + 2)/(-1(1sin(2πx) - 2) + 2) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -2|(-3|((1x + 1)/(3x - 2)) - 2| - 1) + 2| + 3 and g(x) = -3(-1sin(1πx - 3) + 1)^2 - 2(-1sin(1πx - 3) + 1) where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -3((-2(-3sin(1πx - 1) - 2) - 3)/(2(-3sin(1πx - 1) - 2) + 1))^2 - 5((-2(-3sin(1πx - 1) - 2) - 3)/(2(-3sin(1πx - 1) - 2) + 1)) + 1 = (-3(1sin(1πx + 3) + 2) + 1)/(-2(1sin(1πx + 3) + 2) - 3) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 4(1cos(1π(-2x - 5) + 1)) and g(x) = (-2(2|x - 1|) + 2)/(3(2|x - 1|) - 1) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 1((-1(-1cos(3πx - 2) + 3) - 1)/(-1(-1cos(3πx - 2) + 3) + 2)) + 1 and g(x) = 1(1sin(3πx - 2) - 2)^2 + 1(1sin(3πx - 2) - 2) + 1 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = (2(2cos(3π((-3x + 1)/(2x - 1)) + 2) - 2) - 2)/(1(2cos(3π((-3x + 1)/(2x - 1)) + 2) - 2)) and g(x) = -2cos(3π((-2x - 3)/(2x + 2)) + 1) + 2 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 2(2cos(2π(-3x^2 - 1x - 3)) - 1) - 1 and g(x) = 2(-1e^(-1x) - 1) + 5 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -3|(2|(-1cos(2πx + 1) + 3) + 1| + 1) - 2| + 2 and g(x) = -1|(3|x - 3| - 1) - 1| + 1 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -1cos(2π(1(1x^2 - 4x - 1)^2 - 2) - 2) - 3 and g(x) = 1cos(2π(-4x + 5)) - 1 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -3cos(3π(-3|(-2x) - 2| + 1) + 1) - 1 = (-2(-1cos(3πx - 3) - 2) - 1)/(3(-1cos(3πx - 3) - 2) + 1) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -3sin(1π(1|((-2x - 3)/(1x - 2)) + 2| + 3)) and g(x) = (-2((-2x - 2)/(-2x - 2)))/(-1((-2x - 2)/(-2x - 2)) - 1) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 1(1(2x) - 3) + 2 = 1sin(1π((2x + 2)/(-3x - 2)) - 3) - 3 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 1(-1sin(2π(3|x + 2| - 3) + 2) + 3)^2 - 2(-1sin(2π(3|x + 2| - 3) + 2) + 3) + 2 and g(x) = -2(-3sin(2πx + 3) - 1) + 2 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -4(2sin(2π(-3|x - 2| - 1) + 3) + 1)^2 + 1(2sin(2π(-3|x - 2| - 1) + 3) + 1) + 4 = 1sin(3π(2x^2 + 4x - 2)) - 3 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 3sin(3π(3(2|x - 2| - 2)^2 - 5(2|x - 2| - 2)) + 2) + 2 and g(x) = (3(2x + 2) - 3)/(-3(2x + 2) - 1) where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -4((-2(1|x - 3| - 2) - 3)/(-1(1|x - 3| - 2) + 3)) - 2 and g(x) = 4(-2|x - 3| + 2) + 5 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 1(1sin(1π((3x - 3)/(3x - 2)) - 3) + 2) - 1 and g(x) = (-2(-2|x| + 3) + 1)/(-3(-2|x| + 3) + 1) where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 2(-3sin(1π((2x - 3)/(-2x + 3)) + 3) + 1)^2 + 3(-3sin(1π((2x - 3)/(-2x + 3)) + 3) + 1) - 2 and g(x) = 2(1cos(1πx + 1) + 3) intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 3|(-2cos(3π(1x^2 - 3x - 5) + 2) - 1) - 1| and g(x) = -3(3x^2 - 4x - 4) + 3 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -2(-4(-1x) + 2)^2 + 4(-4(-1x) + 2) - 3 = 2sin(2π(-4x + 2) + 1) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 5(1|(2sin(3πx + 3) + 3) - 3| + 3) + 5 = 4(2cos(3πx) + 3)^2 - 4(2cos(3πx) + 3) + 2 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -2sin(3π(-1(-2x^2 - 1x + 5)) + 2) - 3 = (1(1e^(-2x) + 3) - 2)/(-1(1e^(-2x) + 3) - 3) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -1e^(2(2(4x)^2 + 5(4x))) - 1 = -2sin(3π(2|x - 3| + 3) + 1) - 1 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -4(-1(-2cos(3πx + 2) - 1)^2 - 4(-2cos(3πx + 2) - 1) - 5)^2 - 5(-1(-2cos(3πx + 2) - 1)^2 - 4(-2cos(3πx + 2) - 1) - 5) - 1 and g(x) = -1|(-1cos(3πx - 2) - 1) - 3| + 1 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -3sin(3π((-2((2x)/(-3x + 4)) - 1)/(1((2x)/(-3x + 4)))) - 3) + 3 = 1(3|x - 2| - 2) - 3 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 1(-2((-1x - 3)/(-2x - 3))^2 - 1) + 4 = -2sin(2π(1|x + 1| - 3) - 2) + 2 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation (2((-1(-3cos(3πx - 1) + 3))/(2(-3cos(3πx - 1) + 3) - 3)) + 2)/(-3((-1(-3cos(3πx - 1) + 3))/(2(-3cos(3πx - 1) + 3) - 3))) = -1sin(1π((-3x)/(1x + 3))) - 2 have for x in the interval [-10, 10]?

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[User]
How many solutions does the equation -1(1cos(1π(5x^2 + 2) + 1) - 3) - 1 = 2sin(3π((3x + 1)/(3x - 2)) - 3) + 2 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation (1(4(1x) - 1) - 3)/(2(4(1x) - 1) + 1) = -2cos(3π(4x - 4)) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = (3(-2sin(3π(-1x - 3))) - 3)/(3(-2sin(3π(-1x - 3)))) and g(x) = (3(-5x - 1) - 2)/(1(-5x - 1) + 2) intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -1cos(2π((3((2x + 2)/(3x + 3)) + 1)/(2((2x + 2)/(3x + 3)) + 3)) + 3) and g(x) = -4(-2cos(2πx - 1) - 1) + 1 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 5(2cos(1π(1|x - 1| - 1) - 2) + 1)^2 - 4(2cos(1π(1|x - 1| - 1) - 2) + 1) + 3 and g(x) = 3e^(1((-1x + 2)/(2x - 1))) + 1 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 5(-2cos(2π(-1|x + 2| + 2)) + 3)^2 - 2(-2cos(2π(-1|x + 2| + 2)) + 3) - 4 and g(x) = (2(-3|x - 3| - 3))/(2(-3|x - 3| - 3) + 1) intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 3e^(1(-2|(-2|x + 1| + 2) + 1| - 3)) + 3 = (1(-1cos(1πx + 2) + 1) + 3)/(-1(-1cos(1πx + 2) + 1) + 2) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = (-3(-3sin(3π((-1x - 3)/(2x - 1)) - 3)) - 2)/(1(-3sin(3π((-1x - 3)/(2x - 1)) - 3))) and g(x) = 5(2|x - 1|) + 5 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -2(5(2|x - 3| - 1) - 5) + 5 and g(x) = 4(3cos(2πx + 1) - 1) - 2 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -3sin(3π(5(2x^2 - 3x + 5)^2 - 5(2x^2 - 3x + 5) - 1) - 1) and g(x) = 2sin(2π(-1x^2 + 1x - 4) - 1) + 2 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = (-2(1|(-1|x| + 3) + 2| - 1) - 1)/(3(1|(-1|x| + 3) + 2| - 1) + 1) and g(x) = 1sin(1π(-3|x + 3| + 1) - 2) - 2 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -2((2(2x^2 + 5x - 2) + 3)/(-1(2x^2 + 5x - 2) + 3))^2 + 3((2(2x^2 + 5x - 2) + 3)/(-1(2x^2 + 5x - 2) + 3)) - 1 = (-3(-3cos(1πx + 3)) + 2)/(-1(-3cos(1πx + 3)) + 2) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = (-2(3|((-2x + 1)/(-1x + 3)) + 1| - 1))/(3(3|((-2x + 1)/(-1x + 3)) + 1| - 1) + 3) and g(x) = 5(1x^2 + 3x - 3)^2 + 4(1x^2 + 3x - 3) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 2cos(3π(1|(-1x^2 + 2x + 5) + 3| + 1) + 3) and g(x) = -2|(3cos(2πx - 2) - 1) + 1| + 2 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 3sin(2π(3|(-5x^2 + 2x - 3) + 1| - 1) + 2) - 2 and g(x) = (1(-4x^2 + 1x - 5) + 3)/(1(-4x^2 + 1x - 5) + 3) intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -2sin(3π(5((-3x + 2)/(3x - 2))^2 + 4((-3x + 2)/(3x - 2)) - 1) + 2) + 1 and g(x) = 4(-2|x| + 1)^2 - 3 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -4(-3(2cos(3πx + 3) + 2) + 2)^2 + 3(-3(2cos(3πx + 3) + 2) + 2) - 2 and g(x) = -2(-3sin(1πx - 2) + 1)^2 + 1(-3sin(1πx - 2) + 1) + 5 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation (1(3cos(1π((3x - 2)/(2x + 3)) - 3) - 2))/(-2(3cos(1π((3x - 2)/(2x + 3)) - 3) - 2) - 1) = (-2(1e^(-1x) + 3) + 2)/(2(1e^(-1x) + 3)) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = (3(-1|(1|x - 2| + 2) - 1|) - 3)/(-2(-1|(1|x - 2| + 2) - 1|) - 2) and g(x) = (1(3sin(3πx + 3) + 1) + 2)/(1(3sin(3πx + 3) + 1) - 3) where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = (1((2(-3sin(1πx - 3) - 3))/(2(-3sin(1πx - 3) - 3) - 1)) + 2)/(3((2(-3sin(1πx - 3) - 3))/(2(-3sin(1πx - 3) - 3) - 1))) and g(x) = (1((2x + 1)/(-1x - 3)) - 1)/(1((2x + 1)/(-1x - 3)) + 3) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 2|(2cos(3π(-5x^2 - 1x - 2) - 1) + 3) + 1| - 3 and g(x) = (1(-3x^2 - 4x + 2) + 2)/(-2(-3x^2 - 4x + 2) - 1) intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -1(3(-1cos(3πx + 2) + 1) - 3)^2 - 2(3(-1cos(3πx + 2) + 1) - 3) + 2 = (2(-3cos(2πx - 3)) + 1)/(-2(-3cos(2πx - 3))) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 3sin(3π(2(1|x - 3| - 1)^2 + 5(1|x - 3| - 1) + 3) - 1) + 3 and g(x) = -2cos(2π(-2|x - 2| - 1) + 3) where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 5((2(1cos(2πx + 3) - 1) + 3)/(-2(1cos(2πx + 3) - 1) - 1))^2 - 1((2(1cos(2πx + 3) - 1) + 3)/(-2(1cos(2πx + 3) - 1) - 1)) - 4 and g(x) = (1((-2x - 1)/(-1x)) + 1)/(3((-2x - 1)/(-1x)) - 2) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 1(2(-1cos(2πx + 2))^2 + 5(-1cos(2πx + 2)) + 2) = 1((2x + 3)/(-1x))^2 - 5((2x + 3)/(-1x)) + 3 have for x in the interval [-10, 10]?

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[User]
Determine the number of intersection points between the functions f(x) = -3sin(1π(-5((1x + 3)/(-2x - 2)) - 4) + 3) + 3 and g(x) = -1|((1x - 1)/(1x + 1)) + 1| + 1 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -4(-3(2|x + 1| - 1)^2 + 4(2|x + 1| - 1) + 1) and g(x) = 2cos(3π((2x - 1)/(-1x)) - 2) - 1 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation (-1(-5(3sin(1πx + 1) + 3)^2 + 5(3sin(1πx + 1) + 3) + 4) + 3)/(2(-5(3sin(1πx + 1) + 3)^2 + 5(3sin(1πx + 1) + 3) + 4) + 2) = -2sin(1π(3x^2 + 5x + 2) - 2) - 3 have for x in the interval [-10, 10]?

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[User]
Find the number of times the graphs of f(x) = 3e^(1(1(-1|x - 2| + 3) - 3)) and g(x) = 2sin(1π(-4x^2 + 1x) + 2) + 3 intersect in the interval [-10, 10].

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[User]
How many solutions does the equation -4(3(-1sin(2πx + 3) + 1) - 1) + 5 = -1(-5x - 3) + 3 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -2(-3sin(3π(2x + 2) + 1) - 2)^2 + 5(-3sin(3π(2x + 2) + 1) - 2) and g(x) = 1(-1sin(2πx) - 1) + 2 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -3cos(2π(1(1x - 2)^2 - 1(1x - 2) + 3)) - 3 and g(x) = 4(-2cos(2πx + 2) - 2) - 2 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 4((1(-2cos(1πx + 2) + 3) - 3)/(3(-2cos(1πx + 2) + 3) - 2)) + 4 = -3(-3sin(3πx + 1) - 3) + 2 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -3(2cos(3π(-3x^2 + 2x + 1) - 2) - 1) + 2 = (-3(1e^(1x) - 3) + 1)/(-2(1e^(1x) - 3) - 2) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -2(-4(1|x - 1| - 2)^2 - 5(1|x - 1| - 2) + 4) and g(x) = 1cos(3π(4x^2 - 3x - 3) - 1) - 3 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -1(1|(-2|x + 3|) + 2| - 1)^2 + 1(1|(-2|x + 3|) + 2| - 1) + 1 = (1(1|x + 1| + 2) - 2)/(-2(1|x + 1| + 2) + 3) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation (-2(3|(-3cos(3πx - 3)) - 1|) + 1)/(3(3|(-3cos(3πx - 3)) - 1|) + 1) = -1|(4x - 3) + 1| + 1 have for x in the interval [-10, 10]?

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[User]
How many points of intersection exist between the functions f(x) = 2|(1(-3sin(3πx) + 1)^2 - 4(-3sin(3πx) + 1) - 2) + 1| - 1 and g(x) = 1e^(-1(5x^2 - 2x - 4)) + 1 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -2sin(1π(-4(-2x + 4)^2 - 3) - 2) - 2 and g(x) = -1|(5x - 4) - 3| - 3 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -4((-3(1x^2 + 4x - 5) + 2)/(-3(1x^2 + 4x - 5) + 2))^2 + 5((-3(1x^2 + 4x - 5) + 2)/(-3(1x^2 + 4x - 5) + 2)) + 4 = -3(3cos(2πx + 3) - 2) - 1 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = (-3(-3(3sin(3πx + 1)) + 4) - 2)/(-1(-3(3sin(3πx + 1)) + 4) - 3) and g(x) = (-1(1|x| + 3) + 3)/(-2(1|x| + 3)) where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 2sin(1π((-1(-3|x - 1| + 1) - 3)/(1(-3|x - 1| + 1) - 2)) - 1) + 2 = 3cos(1π((-3x + 1)/(1x)) - 3) + 2 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 1(-3sin(2π(1|x + 3| - 3) + 3) - 1) + 2 = (1(2x^2 + 1x - 4) + 3)/(-1(2x^2 + 1x - 4) - 2) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 1cos(1π(-1((1x - 3)/(-3x))^2 + 2((1x - 3)/(-3x)) + 5) - 1) + 2 and g(x) = 1|(-3x + 4) - 1| intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -1|(5(-2x - 5) - 4) - 2| and g(x) = -4(2cos(3πx + 1))^2 - 5(2cos(3πx + 1)) + 1 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -2|((2(3sin(1πx - 1) + 1) - 3)/(-2(3sin(1πx - 1) + 1) - 1))| + 1 and g(x) = 3(-1|x + 2| + 3)^2 - 4 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -2(1(2x - 4) - 5) - 2 and g(x) = 5(-1sin(2πx - 3) + 1)^2 - 1(-1sin(2πx - 3) + 1) - 2 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = (-3(-2sin(2π(-2x^2 + 5x - 4) + 2) + 2) - 1)/(2(-2sin(2π(-2x^2 + 5x - 4) + 2) + 2) + 1) and g(x) = -5((2x + 3)/(-3x)) - 3 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = (-1(-1((-3x)/(2x + 2))^2 + 4((-3x)/(2x + 2)) - 1) + 3)/(3(-1((-3x)/(2x + 2))^2 + 4((-3x)/(2x + 2)) - 1)) and g(x) = -3(1x^2 - 1x)^2 - 2(1x^2 - 1x) + 4 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 1cos(2π(-3(-2|x + 1| + 3)^2 + 3(-2|x + 1| + 3) + 1) - 1) = -1(3sin(2πx + 1) + 2)^2 - 4(3sin(2πx + 1) + 2) + 5 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -5(-1cos(3π(5x^2 + 2x - 2) + 3)) + 5 and g(x) = (-3(-3sin(1πx + 2) - 1) + 2)/(-1(-3sin(1πx + 2) - 1) + 3) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = (-3(1(-3cos(3πx - 1) - 1)^2 + 5(-3cos(3πx - 1) - 1) + 1) + 3)/(2(1(-3cos(3πx - 1) - 1)^2 + 5(-3cos(3πx - 1) - 1) + 1) + 1) and g(x) = 1(4x - 2) - 2 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 1(2cos(2π(3x) - 2) + 3)^2 - 5(2cos(2π(3x) - 2) + 3) + 1 = 2sin(1π((-3x)/(-2x - 1)) + 2) + 2 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 3(2sin(3π(5x^2 + 1x + 5) + 1) - 1)^2 + 5(2sin(3π(5x^2 + 1x + 5) + 1) - 1) + 1 and g(x) = -2e^(-2(3x)) + 2 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 2e^(1(-5(2|x - 3| + 1) - 2)) and g(x) = 2|(-2x^2 + 1x + 5) - 1| - 1 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = (3(3|(-1sin(1πx - 1) + 3) - 1| - 1) + 1)/(1(3|(-1sin(1πx - 1) + 3) - 1| - 1) - 3) and g(x) = 1|(4x^2 + 3x - 2) - 1| - 2 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -1cos(3π(2(4x^2 + 2x + 2) + 1) - 3) - 2 and g(x) = 3((1x)/(1x - 2)) - 3 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -3((2(5x^2 - 1x + 4) + 3)/(-3(5x^2 - 1x + 4) + 4))^2 + 4((2(5x^2 - 1x + 4) + 3)/(-3(5x^2 - 1x + 4) + 4)) - 1 and g(x) = -1(-2|x - 2| + 3)^2 + 2 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -1(2|(-2|x + 2| + 1) - 2| + 2) + 1 and g(x) = -3|(-3sin(1πx + 2))| in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = (-2(-3|(-3x^2 - 4x - 2) + 1| - 1) + 2)/(1(-3|(-3x^2 - 4x - 2) + 1| - 1) + 2) and g(x) = -3|(-1x - 4) - 1| + 2 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 2sin(3π((-2((2x)/(2x + 3)) + 2)/(-1((2x)/(2x + 3)) + 3)) + 1) - 1 and g(x) = 4(-3sin(3πx - 2) + 1) + 2 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = (-3(-2(-2x^2 + 5x - 5) + 1))/(2(-2(-2x^2 + 5x - 5) + 1) + 1) and g(x) = -1|(4x^2 + 5x - 3) - 3| + 1 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = (3(-1sin(3π(-1x + 1) - 3) - 2))/(-1(-1sin(3π(-1x + 1) - 3) - 2) + 2) and g(x) = 1(-2x^2 + 5x - 1)^2 - 2(-2x^2 + 5x - 1) - 2 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 5(-2sin(3π(2x - 4) + 1) + 2)^2 + 1(-2sin(3π(2x - 4) + 1) + 2) - 3 and g(x) = -3((2x - 1)/(2x + 2))^2 - 2((2x - 1)/(2x + 2)) + 5 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -3((3(2sin(2πx) + 1))/(3(2sin(2πx) + 1) + 3))^2 + 1((3(2sin(2πx) + 1))/(3(2sin(2πx) + 1) + 3)) + 3 = -2e^(-1(-3|x - 3| + 1)) + 2 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 5(3(-1cos(2πx - 3))^2 + 4(-1cos(2πx - 3)) + 1) - 3 and g(x) = -1sin(1π(3|x - 2| + 3) + 1) intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -3(-2sin(2π(1x + 1)) - 2)^2 + 3(-2sin(2π(1x + 1)) - 2) - 1 = (3(-1|x + 3| - 1) - 3)/(1(-1|x + 3| - 1) + 2) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -3(-2e^(-2(-1x^2 + 4x - 3)) + 3)^2 + 3(-2e^(-2(-1x^2 + 4x - 3)) + 3) + 5 and g(x) = 1cos(3π(-5x + 3) - 1) - 2 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -2((-1((-1x + 1)/(-3x + 4)) - 3)/(1((-1x + 1)/(-3x + 4)) - 2)) + 2 = -3|(-4x^2 - 5x + 4)| - 1 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = (-2(-5(4x^2 + 1x - 4) + 5) + 3)/(2(-5(4x^2 + 1x - 4) + 5) - 1) and g(x) = 4(-2cos(2πx + 1) + 3)^2 - 4(-2cos(2πx + 1) + 3) - 5 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = (-1(3|(-4x + 1) - 1| + 3) - 1)/(1(3|(-4x + 1) - 1| + 3) + 2) and g(x) = (2(-3cos(1πx - 3) + 2) - 1)/(-3(-3cos(1πx - 3) + 2) + 4) where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 2(-1|(-2x - 1) - 1| + 2) + 4 = -1cos(2π(5x + 4)) + 2 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 3|(-1|((-1x + 2)/(3x + 2)) + 3| + 2) + 2| and g(x) = (-1(-3sin(3πx + 1) + 3) - 3)/(3(-3sin(3πx + 1) + 3) - 2) intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -2((-3(1|x + 1| - 2) + 3)/(-2(1|x + 1| - 2)))^2 - 1((-3(1|x + 1| - 2) + 3)/(-2(1|x + 1| - 2))) - 1 and g(x) = (2(5x^2 - 4x + 4) + 2)/(-2(5x^2 - 4x + 4) - 3) intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -1(-3sin(3π(-1|x + 3| + 2) + 3) - 3)^2 + 5 and g(x) = -2e^(-1(-1x - 5)) - 1 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = (1(2(1x^2 - 3x - 5) - 1) + 1)/(3(2(1x^2 - 3x - 5) - 1) + 1) and g(x) = -2|(4x^2 - 4x - 3) - 3| + 1 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -3sin(2π((1(-1x^2 + 1x))/(2(-1x^2 + 1x) + 3))) - 1 and g(x) = 4(-2x^2 - 5x - 1)^2 + 4(-2x^2 - 5x - 1) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = (1(-3(-1cos(2πx + 1) - 2)^2 + 5))/(3(-3(-1cos(2πx + 1) - 2)^2 + 5) - 2) and g(x) = (-2(-3x - 3))/(1(-3x - 3) - 2) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -3|(-5((2x + 2)/(-2x + 3)) - 4) - 2| + 3 and g(x) = -1cos(1π(3x^2 - 2x + 3) + 2) intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -2(1|((2x + 1)/(2x + 2)) - 2| - 2) - 1 and g(x) = -3(-2sin(3πx - 2) + 1)^2 - 3(-2sin(3πx - 2) + 1) - 1 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 3cos(3π(-1|((-3x - 1)/(1x + 1)) + 3| - 1) + 3) + 3 = (1(-2e^(-2x) + 2) - 3)/(-3(-2e^(-2x) + 2) + 2) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -3cos(1π(-2|(-3|x - 1|) - 2| - 1) + 2) - 2 and g(x) = 1((3x - 2)/(-1x - 2))^2 + 2((3x - 2)/(-1x - 2)) where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = (-1(-3|(1x^2 + 1x - 2) + 3| + 2))/(-2(-3|(1x^2 + 1x - 2) + 3| + 2) + 3) and g(x) = -5(2sin(1πx) - 1) + 2 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = (1((-1((2x)/(2x - 3)) - 1)/(-1((2x)/(2x - 3)) + 2)) + 1)/(2((-1((2x)/(2x - 3)) - 1)/(-1((2x)/(2x - 3)) + 2)) + 3) and g(x) = -2cos(2π((-2x + 2)/(1x + 1)) - 1) + 2 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 1|((-3((-1x + 2)/(-1x - 1)))/(2((-1x + 2)/(-1x - 1)) - 1)) + 2| - 3 and g(x) = 3(2sin(3πx - 3) + 1) - 5 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = (-3(3(-1x^2 + 5x)^2 - 4(-1x^2 + 5x) + 5) - 1)/(1(3(-1x^2 + 5x)^2 - 4(-1x^2 + 5x) + 5) - 3) and g(x) = 1(2sin(2πx - 1)) - 4 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -2(3|((-1x + 3)/(1x)) + 1| - 2)^2 - 2(3|((-1x + 3)/(1x)) + 1| - 2) - 1 and g(x) = -2(-1x^2 + 4x + 1)^2 - 2(-1x^2 + 4x + 1) + 2 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = (-1(4((-3x)/(-2x + 3))^2 - 3))/(-1(4((-3x)/(-2x + 3))^2 - 3)) and g(x) = 5(-1x^2 - 2x + 2)^2 - 3(-1x^2 - 2x + 2) - 4 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation (-3(2cos(2π(-2x + 3) + 2)))/(2(2cos(2π(-2x + 3) + 2)) - 1) = -1(2x^2 - 2x)^2 - 4(2x^2 - 2x) - 5 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation (2(-3|(-1|x + 3| - 1) + 2| - 1) + 3)/(3(-3|(-1|x + 3| - 1) + 2| - 1) + 2) = (-2(3sin(2πx + 1)) - 2)/(-1(3sin(2πx + 1))) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -1(-5((2x + 1)/(-3x + 4))^2 - 5((2x + 1)/(-3x + 4)) - 1)^2 + 4(-5((2x + 1)/(-3x + 4))^2 - 5((2x + 1)/(-3x + 4)) - 1) + 3 and g(x) = -5(-1cos(2πx - 3) - 1)^2 + 5(-1cos(2πx - 3) - 1) + 4 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 3cos(1π((1(2x + 1) + 1)/(2(2x + 1) - 1)) + 3) + 3 and g(x) = (-1((3x + 2)/(2x + 1)))/(-1((3x + 2)/(2x + 1)) - 1) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -1((-3(-1|x - 2| + 2) - 1)/(1(-1|x - 2| + 2) + 3)) - 5 = -1cos(1π(-2|x + 1| - 2) - 1) - 1 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -3cos(2π(1|(-2x - 5) - 2|) + 3) - 2 and g(x) = -3sin(1π(4x - 3) - 1) + 3 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation (1(-2sin(2π((-3x + 2)/(-3x + 4)) + 1) + 2) - 3)/(-1(-2sin(2π((-3x + 2)/(-3x + 4)) + 1) + 2) - 2) = 2sin(2π(3|x - 3| - 1) + 1) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -3|((-1(-2|x - 3|) - 2)/(-3(-2|x - 3|))) + 1| - 3 = -2sin(3π(-5x - 4)) - 3 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 2|(-4(-5x)^2 + 4(-5x) + 5) - 1| - 1 and g(x) = -3e^(1(1|x - 2| - 3)) + 3 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 1(2e^(2(-3x - 1)) - 1)^2 + 1(2e^(2(-3x - 1)) - 1) + 2 = 2sin(2π(2x - 4) + 3) + 2 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = (-2((-3(-3|x + 2| + 2) - 3)/(-3(-3|x + 2| + 2) + 2)))/(-2((-3(-3|x + 2| + 2) - 3)/(-3(-3|x + 2| + 2) + 2)) + 1) and g(x) = -3sin(1π(2x - 3) - 1) where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 1(2(-3x - 4) - 1)^2 - 1(2(-3x - 4) - 1) and g(x) = 3sin(2π(1x^2 - 1x + 4) - 3) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -3|((1(5x^2 + 2x + 3))/(2(5x^2 + 2x + 3))) + 3| + 1 = 5(-3sin(3πx + 2) - 1) - 1 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -3cos(3π(-1(5x + 2) - 1) - 2) and g(x) = 1sin(2π(3x) + 1) + 1 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -5(-3(2|x - 1| - 1) + 4)^2 + 5 = -1|(4x) - 1| - 3 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 5((-1(2|x - 1| - 3) + 2)/(1(2|x - 1| - 3) + 1))^2 - 3((-1(2|x - 1| - 3) + 2)/(1(2|x - 1| - 3) + 1)) - 1 and g(x) = 3cos(2π(-4x^2 + 4x) - 3) + 3 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 3(2e^(-2(3x + 3))) - 2 and g(x) = 1sin(2π(5x^2 - 4x + 2) + 1) - 2 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = (-3(3((1x - 1)/(-1x - 2)) + 5))/(2(3((1x - 1)/(-1x - 2)) + 5) + 3) and g(x) = -3sin(3π((-3x - 2)/(-1x - 3)) + 2) - 3 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 3sin(2π(3|(-3|x - 1|) + 2| + 1) + 2) + 3 and g(x) = 1|((3x + 3)/(3x + 2)) + 1| - 2 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -2sin(2π(1|(-2|x - 2| - 1) + 1|) + 3) - 1 and g(x) = -3|(-5x^2 + 2x + 2) + 3| - 1 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 1|(-1|((2x + 1)/(-1x)) + 1| + 1) + 2| and g(x) = 3|(3cos(2πx - 3) - 1) - 3| - 2 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -3|(3sin(1π(-1|x - 2| - 3) - 1) + 2) + 2| and g(x) = 2(-2|x - 3| - 2) + 4 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 4(1|(1|x + 1|) - 3| + 2) - 5 = 4(-3cos(3πx - 3) + 1)^2 + 1(-3cos(3πx - 3) + 1) + 3 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = (1(1(-3|x + 3| + 2) + 5) + 1)/(2(1(-3|x + 3| + 2) + 5) + 1) and g(x) = 3sin(3π(-3|x + 2| - 1) - 3) - 1 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 3((1(-1x^2 - 1))/(-1(-1x^2 - 1) - 1))^2 + 2((1(-1x^2 - 1))/(-1(-1x^2 - 1) - 1)) = 4(-3cos(2πx + 1) + 1) - 3 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 1(-3sin(1π((-3x + 1)/(2x)) - 1) - 1)^2 - 4(-3sin(1π((-3x + 1)/(2x)) - 1) - 1) + 1 and g(x) = (1(-1x + 1))/(-1(-1x + 1) - 1) intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = (-3(-3|(2|x| + 3) - 2| + 1) + 1)/(-3(-3|(2|x| + 3) - 2| + 1) + 1) and g(x) = -1cos(3π(1x^2 - 1x - 3) + 2) + 2 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = (3(-1|(3cos(1πx + 1) + 3)| + 3))/(-1(-1|(3cos(1πx + 1) + 3)| + 3) + 2) and g(x) = 3|(3sin(3πx) + 2) + 2| + 3 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation (2(-3(-2sin(2πx + 2)) + 3) + 2)/(2(-3(-2sin(2πx + 2)) + 3) + 3) = (1(1cos(2πx + 2) + 1))/(-3(1cos(2πx + 2) + 1) + 2) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 1|(1(2x - 4) - 1) + 3| + 1 and g(x) = -1cos(1π(2|x| + 1) + 3) + 3 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 4(1cos(1π((-1x - 3)/(-3x)) - 1))^2 + 2(1cos(1π((-1x - 3)/(-3x)) - 1)) + 3 and g(x) = 2cos(1π(-2|x + 3|) - 3) + 1 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -1(1cos(2π(1|x| + 3) - 1) - 2) - 4 and g(x) = 1|(-2|x + 3| + 2) + 3| - 2 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -5(-2cos(1π(3|x + 1| + 3) + 3) + 1) - 5 and g(x) = -1|(-5x - 4) - 2| - 2 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = (2((-2(1cos(2πx - 3) - 1) - 1)/(-3(1cos(2πx - 3) - 1))) + 1)/(2((-2(1cos(2πx - 3) - 1) - 1)/(-3(1cos(2πx - 3) - 1))) + 1) and g(x) = 1cos(1π((3x - 3)/(2x + 2))) + 2 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = (2((-1(-5x + 1) + 1)/(3(-5x + 1) + 3)) - 2)/(1((-1(-5x + 1) + 1)/(3(-5x + 1) + 3)) + 1) and g(x) = 3(-2cos(3πx + 3) - 1) - 2 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 2(1|((-2x)/(2x + 1)) + 3| - 2)^2 + 1(1|((-2x)/(2x + 1)) + 3| - 2) - 1 and g(x) = 5(-2x - 5)^2 - 5(-2x - 5) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 3((1(1e^(1x) - 2) + 1)/(3(1e^(1x) - 2) - 2)) - 1 and g(x) = -3(-3cos(2πx - 2) + 1)^2 + 3(-3cos(2πx - 2) + 1) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 4(4(-1|x - 1|)^2 - 2(-1|x - 1|) - 5)^2 - 3(4(-1|x - 1|)^2 - 2(-1|x - 1|) - 5) + 5 and g(x) = 1((3x - 2)/(1x - 3))^2 - 5((3x - 2)/(1x - 3)) where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -2|((-1((1x - 1)/(-2x + 3)))/(-3((1x - 1)/(-2x + 3)) + 2))| - 1 and g(x) = -1|((-1x)/(1x - 3)) + 2| intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 2(2cos(2π(4x^2 + 3x) - 1) + 1)^2 + 3(2cos(2π(4x^2 + 3x) - 1) + 1) + 4 and g(x) = 3cos(2π(-2|x + 1|) + 1) where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = (3(1|((3x + 2)/(-2x)) + 2| + 2) - 1)/(2(1|((3x + 2)/(-2x)) + 2| + 2) + 3) and g(x) = 2cos(3π(-3x + 1) + 1) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = (2(4(-1|x| + 1) - 1) - 1)/(-2(4(-1|x| + 1) - 1) - 2) and g(x) = -1cos(3π((-1x + 2)/(3x - 2)) + 3) + 1 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 2|(2|((3x)/(-3x - 2)) + 1| - 3) + 2| - 1 = (1(-1sin(1πx - 2)) - 2)/(-1(-1sin(1πx - 2)) + 3) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 2sin(1π(5(-1x^2 - 2x - 5) - 2) + 1) and g(x) = -1(-1|x - 2| + 3)^2 - 2(-1|x - 2| + 3) - 2 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -2|(-1cos(3π(-4x^2 - 2x + 4) + 2) - 1) + 1| and g(x) = (-2(4x^2 - 5x + 2) + 2)/(2(4x^2 - 5x + 2) + 3) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 2e^(-1(-2|(5x^2 - 4x - 4)| - 1)) - 3 and g(x) = 4(-1cos(2πx + 1) + 1) - 2 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 4(-2(1cos(1πx + 2) + 2)^2 + 4(1cos(1πx + 2) + 2) + 4)^2 + 1(-2(1cos(1πx + 2) + 2)^2 + 4(1cos(1πx + 2) + 2) + 4) - 2 and g(x) = 1(3|x - 1| - 1) - 1 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 5(2(3cos(3πx + 3) + 2)^2 - 4(3cos(3πx + 3) + 2))^2 - 2 and g(x) = 1sin(1π(5x + 2) - 3) + 3 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = (3(4(1x - 4)^2 + 1(1x - 4) - 4))/(1(4(1x - 4)^2 + 1(1x - 4) - 4) + 2) and g(x) = -3sin(1π(3|x + 3| + 3) - 2) where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 3|(-1|(1|x - 2| - 3) + 2|)| + 1 and g(x) = -2|(2sin(3πx + 3) + 2) - 2| + 3 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 2(1e^(-1(3x^2 - 1x - 5)) + 3) + 2 = 1(3cos(1πx + 2) + 2) + 3 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 2|(2|(2|x + 3| + 1) - 2|)| + 3 and g(x) = (-1(-3sin(3πx - 1) - 2) - 3)/(3(-3sin(3πx - 1) - 2) - 2) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 2|(-1(-1cos(2πx) + 2)^2 + 2(-1cos(2πx) + 2)) + 1| + 2 = 2((2x - 2)/(1x + 2)) + 2 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -3|(-3|(-5x + 2) - 3| + 3)| = -3cos(2π(-2x^2 + 1x + 2) + 1) - 3 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -4((-3(-3x) + 1)/(1(-3x) - 3))^2 - 5((-3(-3x) + 1)/(1(-3x) - 3)) - 3 and g(x) = -2|((-2x - 1)/(1x + 3)) + 2| where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 1sin(2π(1(-4x - 4)^2 + 2(-4x - 4) + 1) + 3) - 3 and g(x) = 1(-2|x - 1| + 1) - 2 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 1(3sin(3π(4x^2 + 2)) - 1)^2 - 3(3sin(3π(4x^2 + 2)) - 1) + 3 = -3cos(2π(-2x^2 - 5) + 2) - 1 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -3cos(2π(-5((3x + 1)/(-1x)) + 3) - 1) + 1 and g(x) = 2e^(-2(1x^2 - 3x - 2)) where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 2(1(3x^2 + 3x + 5) - 2) - 4 = 3|(-3cos(3πx - 3) + 3) - 2| + 3 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -3|((-3(3x^2 - 5x + 2) + 1)/(2(3x^2 - 5x + 2))) - 2| and g(x) = (-1(-1e^(-2x) - 3) + 1)/(2(-1e^(-2x) - 3) - 1) intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 1cos(2π(-3(-3|x + 1| + 2) + 2) + 2) and g(x) = -2sin(3π(1x + 5) - 3) - 1 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -2(1|((-3x - 3)/(-2x - 1)) - 2| - 2) + 1 and g(x) = 1(1sin(1πx + 1) + 2)^2 - 1(1sin(1πx + 1) + 2) - 1 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation (2(1(3|x + 2| - 2) + 2) - 2)/(3(1(3|x + 2| - 2) + 2) + 1) = 3sin(2π(2|x - 1| - 3) - 2) + 1 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = (-2(1(1sin(2πx - 1) + 3)^2 + 3(1sin(2πx - 1) + 3) - 1) - 3)/(1(1(1sin(2πx - 1) + 3)^2 + 3(1sin(2πx - 1) + 3) - 1) - 3) and g(x) = -3|(-1sin(2πx - 2) + 1) - 2| + 2 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -3sin(1π(-1((-1x + 1)/(2x)) + 1) - 3) - 2 and g(x) = -3sin(2π(-4x^2 + 2x + 3) + 3) + 3 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 3(-1(3|x + 2|) - 4) and g(x) = (-3(-2sin(1πx + 3) - 1))/(-1(-2sin(1πx + 3) - 1) - 2) where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -3cos(1π(-2|(-5x^2 + 4x) + 3| - 3)) + 1 and g(x) = -2cos(1π(-2x^2 + 1x + 5) - 2) + 1 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = (1(-3sin(2π(-1|x + 1| - 3) + 3) + 3) - 1)/(-2(-3sin(2π(-1|x + 1| - 3) + 3) + 3)) and g(x) = (-1(2sin(1πx + 3) + 2) - 3)/(-2(2sin(1πx + 3) + 2) - 2) intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = (1((2(1x - 1) - 2)/(-3(1x - 1) - 3)) - 3)/(3((2(1x - 1) - 2)/(-3(1x - 1) - 3)) + 2) and g(x) = 1sin(1π(-2|x + 3| - 3) + 1) + 1 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -5(2(3|x - 1| - 3))^2 + 2(2(3|x - 1| - 3)) and g(x) = 1e^(-2(1x + 2)) - 1 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 4(1cos(3π((2x - 2)/(2x + 2)) - 1) - 2)^2 + 5(1cos(3π((2x - 2)/(2x + 2)) - 1) - 2) + 1 and g(x) = 3((1x + 2)/(3x + 2)) + 5 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -2sin(2π(-3|(-1x^2 + 3x + 2) + 3| + 3) + 3) + 2 = -1(-1x^2 + 2x + 1)^2 - 4(-1x^2 + 2x + 1) - 1 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -2|(1(-1cos(2πx - 2) - 1) - 1) - 3| and g(x) = -3|(-2e^(1x) + 2) + 3| + 3 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = (-3(-2|(-4x + 1)| + 1) - 1)/(3(-2|(-4x + 1)| + 1) + 1) and g(x) = -2(1|x + 3|)^2 + 4(1|x + 3|) - 2 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 2|((-2(-5x + 3) + 3)/(1(-5x + 3))) - 2| - 1 and g(x) = 3|((-2x + 3)/(-3x + 4))| - 1 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -1cos(1π(-2(4x^2 - 5x)^2 - 5(4x^2 - 5x) + 1) + 2) + 2 and g(x) = -3sin(3π((1x + 1)/(-1x - 3))) + 2 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = (3(-3sin(2π(4x + 5))) - 1)/(2(-3sin(2π(4x + 5))) + 3) and g(x) = -1cos(1π(5x - 2) - 3) where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 2(1(-1|x + 3| - 1)^2 + 1(-1|x + 3| - 1) - 1)^2 - 2(1(-1|x + 3| - 1)^2 + 1(-1|x + 3| - 1) - 1) - 4 and g(x) = (-2(1cos(1πx)))/(2(1cos(1πx)) + 2) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 2|((-3(-2e^(2x) - 2) - 3)/(-1(-2e^(2x) - 2) + 2)) + 1| and g(x) = 5(-2cos(3πx + 1) - 3)^2 - 1(-2cos(3πx + 1) - 3) - 4 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -2|(3(3cos(3πx - 2) + 1) - 3)| - 2 and g(x) = 2(-3|x - 3| + 1) - 2 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -3(-3sin(1π(-4x + 3)) - 2) + 4 and g(x) = -2e^(-2((-1x - 1)/(-3x + 2))) + 3 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 3cos(3π(-3|(-2|x - 1| - 1) - 2|)) = (-2(-1sin(3πx - 3)))/(2(-1sin(3πx - 3)) + 2) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 5(-2sin(1π((-2x + 1)/(-3x)) + 1) + 1)^2 - 2(-2sin(1π((-2x + 1)/(-3x)) + 1) + 1) + 2 and g(x) = (3(2e^(2x) - 2) - 3)/(3(2e^(2x) - 2) + 1) intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -2(-1cos(1π(-1|x| + 1) + 1) - 1) + 1 and g(x) = -2sin(3π(-5x + 2) - 1) + 3 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -1(1(-1x - 4)^2 + 4(-1x - 4) + 3)^2 + 5(1(-1x - 4)^2 + 4(-1x - 4) + 3) - 2 = -2(2|x + 2| + 2) + 2 have for x in the interval [-10, 10]?

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[User]
How many points of intersection exist between the functions f(x) = 2sin(1π(-1((3x + 1)/(-2x + 1))^2 + 1((3x + 1)/(-2x + 1)) - 4) - 2) and g(x) = (-1(3|x + 2| + 1) - 3)/(-2(3|x + 2| + 1) + 3) in the range -10 ≤ x ≤ 10?

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[User]
How many points of intersection exist between the functions f(x) = 3|(-2|(-1|x + 3| + 2)| + 1) - 1| - 3 and g(x) = 1|(-1x - 5)| + 3 in the range -10 ≤ x ≤ 10?

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[User]
How many solutions does the equation (3(1(1x) + 1) - 3)/(-1(1(1x) + 1) - 1) = 3cos(3π(-1|x + 2| - 2) + 1) - 2 have for x in the interval [-10, 10]?

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[User]
How many points of intersection exist between the functions f(x) = -2cos(3π(-1(3x + 2)^2 - 4)) - 3 and g(x) = 2cos(3π(-3x - 3) + 1) - 2 in the range -10 ≤ x ≤ 10?

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[User]
Find the number of times the graphs of f(x) = -1|(-2((-3x + 2)/(-2x - 3))^2 - 1((-3x + 2)/(-2x - 3))) - 3| and g(x) = 3(-2sin(2πx)) + 2 intersect in the interval [-10, 10].

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[User]
Determine the number of intersection points between the functions f(x) = (2(3sin(3π(1x^2 + 2) - 2)) - 3)/(2(3sin(3π(1x^2 + 2) - 2)) + 2) and g(x) = -2((3x - 3)/(-1x - 3)) + 1 where -10 ≤ x ≤ 10.

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[User]
Find the number of times the graphs of f(x) = (-1(-2|(-3sin(2πx + 1)) + 3| + 3) + 2)/(-2(-2|(-3sin(2πx + 1)) + 3| + 3) + 1) and g(x) = -2sin(1π(-1x^2 + 5x + 5) + 2) + 1 intersect in the interval [-10, 10].

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[User]
Determine the number of intersection points between the functions f(x) = -2|(-5(-1x^2 + 4x + 3) + 5) + 3| and g(x) = 4(-3|x + 1|) - 5 where -10 ≤ x ≤ 10.

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[User]
Determine the number of intersection points between the functions f(x) = 4((1((2x)/(3x - 1)) - 1)/(2((2x)/(3x - 1)) - 1))^2 - 3((1((2x)/(3x - 1)) - 1)/(2((2x)/(3x - 1)) - 1)) - 5 and g(x) = -1|(3cos(2πx - 3) + 2) - 2| - 3 where -10 ≤ x ≤ 10.

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[User]
Determine the number of intersection points between the functions f(x) = (-2(-2cos(2π(-3|x| + 3) - 2) + 2) + 3)/(-3(-2cos(2π(-3|x| + 3) - 2) + 2) + 1) and g(x) = 2|(1e^(-2x) + 1) - 1| + 2 where -10 ≤ x ≤ 10.

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[User]
Determine the number of intersection points between the functions f(x) = -3sin(2π(-1(3x^2 - 5x - 1) - 2) - 1) + 2 and g(x) = 2((-2x - 3)/(-3x - 2)) - 4 where -10 ≤ x ≤ 10.

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[User]
How many points of intersection exist between the functions f(x) = -3(2sin(2π(3|x - 2| + 3) - 2) - 1) - 4 and g(x) = 2|(2|x + 2| + 3)| - 3 in the range -10 ≤ x ≤ 10?

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[User]
Determine the number of intersection points between the functions f(x) = 1(-3cos(3π(-1|x - 2| - 1))) - 3 and g(x) = 1|(2e^(-1x) - 3)| - 1 where -10 ≤ x ≤ 10.

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[User]
Find the number of times the graphs of f(x) = 1|(-4((1x + 3)/(-1x + 3)) + 1) + 2| - 3 and g(x) = -1|((-3x)/(-3x - 2)) - 2| + 2 intersect in the interval [-10, 10].

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[User]
Determine the number of intersection points between the functions f(x) = -3e^(-1(2|(1x^2 - 1x + 3) + 3| + 2)) and g(x) = 2|(-2|x|) + 3| - 1 where -10 ≤ x ≤ 10.

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[User]
Find the number of times the graphs of f(x) = (-3(-5(-4x^2 + 4x + 3) + 2) + 3)/(3(-5(-4x^2 + 4x + 3) + 2) + 2) and g(x) = 3cos(3π(1|x - 2| - 2) + 1) - 1 intersect in the interval [-10, 10].

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[User]
Determine the number of intersection points between the functions f(x) = 3e^(-1((1(-1|x + 1| + 3) + 1)/(-1(-1|x + 1| + 3)))) + 1 and g(x) = 4(2cos(1πx + 2) + 1) - 4 where -10 ≤ x ≤ 10.

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[User]
Determine the number of intersection points between the functions f(x) = 2(3cos(3π(1|x + 1| - 1) - 1) + 1) - 1 and g(x) = (-1(-5x^2 + 4x - 3) + 1)/(3(-5x^2 + 4x - 3) + 1) where -10 ≤ x ≤ 10.

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[User]
Determine the number of intersection points between the functions f(x) = 3|(1sin(3π(-1x^2 - 3x - 1) + 2) - 1)| + 2 and g(x) = 2sin(1π(-1|x + 3| + 1)) + 2 where -10 ≤ x ≤ 10.

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[User]
Determine the number of intersection points between the functions f(x) = -3(1(3cos(2πx - 3) + 1) + 2)^2 - 1(1(3cos(2πx - 3) + 1) + 2) + 3 and g(x) = (2((-1x)/(-1x - 3)) + 1)/(-2((-1x)/(-1x - 3)) - 1) where -10 ≤ x ≤ 10.

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[User]
Find the number of times the graphs of f(x) = 3cos(3π(-2(2|x + 2| - 2)^2 - 5(2|x + 2| - 2))) - 1 and g(x) = 3((-2x + 3)/(3x)) + 5 intersect in the interval [-10, 10].

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[User]
Find the number of times the graphs of f(x) = 1|(-3sin(1π(4x^2 + 1x + 5) + 1) + 2) - 2| + 1 and g(x) = (-2(4x^2 - 1x - 3) + 1)/(1(4x^2 - 1x - 3) - 3) intersect in the interval [-10, 10].

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