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

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


[User]
How many solutions does the equation 1(3|(4x^2 - 1x - 5) - 3| - 2)^2 - 1 = (-1(-3sin(1πx) - 3) + 3)/(-1(-3sin(1πx) - 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((1(2e^(2x)))/(-1(2e^(2x)) - 2)) + 1)/(-2((1(2e^(2x)))/(-1(2e^(2x)) - 2)) + 3) and g(x) = -2sin(2π(5x^2 - 3x + 5)) + 1 where -10 ≤ x ≤ 10.

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


[User]
How many solutions does the equation 3((-3((2x - 3)/(-2x - 2)) - 1)/(-3((2x - 3)/(-2x - 2)) + 1)) - 2 = -2sin(1π(5x - 5) - 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(5((3x + 2)/(-3x + 2)) + 5) - 3)/(1(5((3x + 2)/(-3x + 2)) + 5) + 3) and g(x) = -1sin(2π(-2x + 3) - 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) = -2(3sin(1π(-3|x - 2| + 1) - 3) + 3)^2 - 3(3sin(1π(-3|x - 2| + 1) - 3) + 3) + 1 and g(x) = (-2((-2x + 3)/(-2x - 2)))/(-1((-2x + 3)/(-2x - 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) = -1(2|(1cos(3πx + 1) - 3) - 3| + 1) + 5 and g(x) = (-2(-3sin(1πx + 2) + 1) - 1)/(-1(-3sin(1πx + 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 2(-2(1x^2 - 5x + 2) - 2)^2 - 1 = 3sin(1π((2x - 2)/(1x)) + 3) - 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 2(2|(3x^2 + 2x - 3) - 3|)^2 - 1(2|(3x^2 + 2x - 3) - 3|) - 2 = (-1(5x - 2))/(-3(5x - 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) = 2|(-2cos(2π(4x + 1) - 1) + 3) - 1| + 2 and g(x) = -2cos(2π(-1x + 1) - 1) + 2 where -10 ≤ x ≤ 10.

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


[User]
How many solutions does the equation -2cos(1π(-2|((-2x - 3)/(2x)) - 3|) - 1) = (-1((1x - 1)/(3x)) + 3)/(3((1x - 1)/(3x))) 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(-4(-1|x + 2| + 2) + 5) - 2) - 2 and g(x) = -2e^(2(-2x - 3)) - 2 where -10 ≤ x ≤ 10.

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


[User]
How many solutions does the equation 2(-3|(2sin(2πx - 1) - 2) + 1| + 3) - 4 = (-3(-3cos(3πx + 2) + 2) - 2)/(-2(-3cos(3πx + 2) + 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) = 1sin(2π(1|(1|x - 1| + 3) + 2| + 3)) and g(x) = (1((-1x + 1)/(1x - 3)) + 2)/(-3((-1x + 1)/(1x - 3)) + 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) = -3|(-2cos(3π(-3x - 2) - 3) - 2)| and g(x) = (-1((-3x - 2)/(-1x + 2)) + 2)/(3((-3x - 2)/(-1x + 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) = -1(1cos(1π(1x - 4) + 2) - 2) - 3 and g(x) = 3sin(3π((3x - 1)/(1x + 2)) - 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) = 4((1(2|x| - 1) + 1)/(2(2|x| - 1) - 3))^2 - 5((1(2|x| - 1) + 1)/(2(2|x| - 1) - 3)) + 1 and g(x) = 2|(-5x^2 - 4x - 2) - 3| + 3 in the range -10 ≤ x ≤ 10?

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


[User]
How many solutions does the equation -1|(5(-3x^2 + 2x + 3) + 2) + 2| + 1 = 1(-3|x| - 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|(3(-1cos(2πx + 1) + 3) + 1) - 3| - 2 and g(x) = 1(-2e^(1x) - 3)^2 + 1(-2e^(1x) - 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) = (1(-4(3x^2 + 4x)^2 + 2(3x^2 + 4x) - 4))/(-3(-4(3x^2 + 4x)^2 + 2(3x^2 + 4x) - 4) + 2) and g(x) = -1cos(3π((-3x)/(3x - 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) = 2|(-1(-1x + 2) - 2) + 3| - 2 and g(x) = -3|(4x^2 - 1x - 1) - 3| + 2 where -10 ≤ x ≤ 10.

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


[User]
How many solutions does the equation -2|(1cos(1π(3|x| + 1) + 2) - 1)| = 2cos(2π(5x^2 + 3) - 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|(2sin(3π(5x^2 - 2x + 5) - 3) - 3) + 1| - 2 and g(x) = 1e^(-1(-4x^2 + 3x - 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) = 1(2cos(3π(1|x - 3|) - 3) - 1)^2 + 5 and g(x) = 2(-3x + 5)^2 - 4(-3x + 5) - 4 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(-3x + 3) + 4) - 1) + 2 = (3(3cos(3πx + 3)) + 2)/(-3(3cos(3πx + 3)) - 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 1(-3(-5x - 3)^2 + 4(-5x - 3) + 5)^2 - 4(-3(-5x - 3)^2 + 4(-5x - 3) + 5) - 3 = 1sin(1π(1x + 1) - 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) = 2sin(2π(5(3|x - 1| - 3)^2 - 4(3|x - 1| - 3) - 1) + 1) and g(x) = -4(-2|x - 3| + 1)^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) = -5(2((-1x + 1)/(-3x - 1)) + 2)^2 - 5(2((-1x + 1)/(-3x - 1)) + 2) and g(x) = -3|(2|x - 3| + 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) = (-3(2(-1|x + 1| + 1)^2 + 3(-1|x + 1| + 1) - 3))/(-3(2(-1|x + 1| + 1)^2 + 3(-1|x + 1| + 1) - 3) + 4) and g(x) = -3|(1|x - 2| - 2) + 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) = 3|(1e^(2(3x^2 - 4)) + 1) - 1| + 1 and g(x) = (-1(-3cos(3πx) - 1) + 2)/(-3(-3cos(3πx) - 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(2(-1x - 1)^2 - 2(-1x - 1) + 4) + 2 = -2sin(3π(3|x + 3|)) - 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(1((1x - 3)/(-3x - 1))^2 + 2((1x - 3)/(-3x - 1)) + 3)^2 + 1(1((1x - 3)/(-3x - 1))^2 + 2((1x - 3)/(-3x - 1)) + 3) + 4 and g(x) = (2(2sin(1πx)) + 1)/(-1(2sin(1πx)) - 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(-1cos(1π(-4x^2 + 3x - 3) - 2) - 1)^2 + 3 and g(x) = 2|(-1x - 2) - 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) = -2sin(3π(3(-1|x - 3| - 1)^2 - 3) + 1) and g(x) = 3sin(2π(-2|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 1|((3(-2cos(2πx + 1) + 2) - 1)/(1(-2cos(2πx + 1) + 2))) - 3| + 1 = -4((-2x - 1)/(-1x + 2))^2 + 1((-2x - 1)/(-1x + 2)) + 4 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|(1(2|x - 2|)) - 3| + 2 = 3(-4x^2 + 4x + 5)^2 + 1(-4x^2 + 4x + 5) + 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) = -1cos(3π(2(-4x) + 5)) - 2 and g(x) = 4(1e^(-1x) - 3)^2 + 4(1e^(-1x) - 3) - 2 intersect in the interval [-10, 10].

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


[User]
How many solutions does the equation -1((-2(2cos(3πx + 1)) + 3)/(1(2cos(3πx + 1))))^2 - 2((-2(2cos(3πx + 1)) + 3)/(1(2cos(3πx + 1)))) - 4 = -1(2|x| + 2)^2 - 3(2|x| + 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) = -2cos(1π(4(-5x^2 + 5x + 1) - 5) - 3) - 3 and g(x) = 2cos(1π(-2x - 5) + 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) = 3(1cos(2π(3|x| - 3)) + 1)^2 - 3(1cos(2π(3|x| - 3)) + 1) + 1 and g(x) = 1cos(1π(-1|x - 2| - 3) + 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(3cos(3π(3|x + 3| - 2) + 2) + 2) - 2)/(-1(3cos(3π(3|x + 3| - 2) + 2) + 2) + 3) and g(x) = -2(-5x - 2)^2 - 4(-5x - 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) = -1cos(2π(2|((3x - 1)/(2x + 1)) + 1| - 1) + 1) and g(x) = -1|(2x^2 - 2) + 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) = -2cos(2π((3(4x - 3) + 3)/(2(4x - 3) + 3)) - 2) + 1 and g(x) = 1(2e^(2x) - 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) = -4(-3|(-1cos(2πx - 3)) + 1|) - 4 and g(x) = 3(-1cos(2πx + 3) - 2)^2 + 2(-1cos(2πx + 3) - 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(2cos(1π(-3x^2 + 5x + 5) + 2) + 1))/(1(2cos(1π(-3x^2 + 5x + 5) + 2) + 1)) and g(x) = -1|(2|x + 2| - 2) - 3| + 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) = 4(-1(-2x + 3)^2 - 3(-2x + 3) + 2)^2 + 2(-1(-2x + 3)^2 - 3(-2x + 3) + 2) + 3 and g(x) = 3e^(-1(-1x + 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) = 3cos(1π(2(-1|x - 3| - 3)^2 - 1(-1|x - 3| - 3))) + 3 and g(x) = 2sin(2π(4x^2 + 4) - 2) + 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) = -1sin(2π((1(1|x + 1| + 1) - 2)/(-1(1|x + 1| + 1) + 2)) + 1) - 1 and g(x) = -3(-3sin(2πx + 3) + 2)^2 - 3(-3sin(2πx + 3) + 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) = -1sin(1π(1(3|x + 3| + 1)^2 + 1) - 2) - 1 and g(x) = 5(3sin(3πx - 3) + 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) = -2cos(1π(-5(4x - 4) - 1) - 3) + 3 and g(x) = 1(5x^2 + 3x + 1)^2 + 1(5x^2 + 3x + 1) - 4 intersect in the interval [-10, 10].

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


[User]
How many solutions does the equation -4((2(-1x + 5) + 2)/(2(-1x + 5) - 1))^2 - 5((2(-1x + 5) + 2)/(2(-1x + 5) - 1)) - 3 = -1(-1sin(3πx + 1) + 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 3(1|(1x - 4) + 1| - 3) + 5 = -2sin(2π(3|x - 1| - 3) + 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(1((-2x + 3)/(1x)) - 4) - 3)/(1(1((-2x + 3)/(1x)) - 4) - 2) and g(x) = 1(4x^2 + 4x - 5)^2 + 5(4x^2 + 4x - 5) - 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(-1cos(1πx - 3) - 2) + 2)/(-1(-1cos(1πx - 3) - 2) + 3))^2 - 5((3(-1cos(1πx - 3) - 2) + 2)/(-1(-1cos(1πx - 3) - 2) + 3)) - 2 = 1((-3x + 2)/(-2x - 1))^2 + 3((-3x + 2)/(-2x - 1)) - 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 -4((1(1x + 2) + 2)/(1(1x + 2) - 2)) + 2 = -2sin(1π(-5x^2 - 5x - 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|(3sin(2π(-5x^2 - 1x - 5) + 1) - 1) - 1| - 2 and g(x) = 1sin(3π(2|x + 2| - 1) - 3) + 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(1(-2|x + 2| + 1)^2 + 4(-2|x + 2| + 1) - 5)^2 + 4(1(-2|x + 2| + 1)^2 + 4(-2|x + 2| + 1) - 5) - 2 and g(x) = -5(-3x + 2) - 4 in the range -10 ≤ x ≤ 10?

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


[User]
How many solutions does the equation -3cos(3π(-1((2x - 3)/(-2x - 1)) + 5) + 2) + 2 = -4((-3x - 1)/(-2x - 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(-1(-1|x + 2| + 3)^2 + 4(-1|x + 2| + 3) - 5) + 5 and g(x) = 1|(3sin(3πx) + 3) + 2| + 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) = -1cos(3π(4(-2x^2 + 5x - 3) - 1) + 3) - 3 and g(x) = 3(1cos(2πx + 3) - 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(-2sin(3πx + 1) + 2)^2 - 5(-2sin(3πx + 1) + 2) + 1)^2 - 5(1(-2sin(3πx + 1) + 2)^2 - 5(-2sin(3πx + 1) + 2) + 1) + 2 and g(x) = -1((-3x - 1)/(3x + 3))^2 - 1((-3x - 1)/(3x + 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) = 1sin(3π(-1|(2x) - 2|) - 3) - 2 and g(x) = 3(1x + 2)^2 - 5 intersect in the interval [-10, 10].

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


[User]
How many solutions does the equation 1e^(-2(-1((2x - 2)/(2x - 1))^2 + 5((2x - 2)/(2x - 1)) + 1)) + 3 = -3cos(1π((2x - 2)/(1x + 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 3cos(1π(2|(-2|x - 2| - 1) - 3| + 1) + 2) - 1 = 1(-2sin(3πx + 3) - 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(-3(-2cos(2πx + 3) + 2)^2 - 4(-2cos(2πx + 3) + 2) + 2) and g(x) = (-2(-1sin(1πx + 3) + 3) + 1)/(3(-1sin(1πx + 3) + 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(2|(2sin(2πx)) + 3| - 3) - 2 and g(x) = -3|(-1x^2 - 5x + 5) - 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) = 3(-2sin(3π((-2x - 2)/(2x - 1)) - 3) + 1) - 3 and g(x) = 3cos(3π(1x^2 + 5x - 1) + 1) - 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) = -1e^(1(-4((2x - 3)/(2x)) + 3)) + 2 and g(x) = -3sin(3π(-1|x| + 2) + 1) - 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) = (-2(-3sin(2π((-1x - 1)/(1x + 2)) + 3) - 1) - 3)/(2(-3sin(2π((-1x - 1)/(1x + 2)) + 3) - 1)) and g(x) = (3((2x + 3)/(2x + 2)) - 2)/(-3((2x + 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) = 4(1|(2|x - 3| - 1) - 1| + 2)^2 - 4(1|(2|x - 3| - 1) - 1| + 2) + 1 and g(x) = (-2(2cos(3πx + 2)) + 3)/(3(2cos(3πx + 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((-2(-1cos(2πx + 3) - 2))/(1(-1cos(2πx + 3) - 2) + 2)) + 1)/(-1((-2(-1cos(2πx + 3) - 2))/(1(-1cos(2πx + 3) - 2) + 2)) + 3) = -1(-2x^2 - 2x + 4) + 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 -3(-1|(4x^2 - 1x - 5)| + 2) - 5 = 3cos(3π(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) = -2sin(2π(-1(3x^2 + 3x - 4)^2 - 2(3x^2 + 3x - 4)) + 2) + 3 and g(x) = -2sin(1π((-2x + 1)/(3x - 1)) - 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) = 3((1(2x + 2) + 3)/(-1(2x + 2)))^2 - 4((1(2x + 2) + 3)/(-1(2x + 2))) - 3 and g(x) = -1cos(3π(3x - 2) + 2) - 3 in the range -10 ≤ x ≤ 10?

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


[User]
How many solutions does the equation -1(-2(-2|x - 3|) - 4) = 2sin(1π(3x^2 + 1) - 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) = 3(-3cos(3π(1|x - 1| + 3) + 2)) + 1 and g(x) = -2(3x + 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(1x^2 - 3x - 1) - 2)^2 - 1(2(1x^2 - 3x - 1) - 2) + 4 and g(x) = -5((-2x - 3)/(2x + 2))^2 + 4((-2x - 3)/(2x + 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) = (-1(-2cos(2π(1x^2 - 4) + 2) + 1) - 1)/(3(-2cos(2π(1x^2 - 4) + 2) + 1) + 1) and g(x) = -1|(1|x + 1| + 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) = 5(3|(2|x - 1| - 3) - 3| - 2) + 2 and g(x) = (-1(-2x^2 + 5x + 3) - 2)/(-3(-2x^2 + 5x + 3) + 4) intersect in the interval [-10, 10].

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


[User]
How many solutions does the equation 1|(-2(-1e^(-1x) + 1)^2 + 2(-1e^(-1x) + 1) + 1) + 3| - 1 = -1cos(2π(3x^2 - 4x + 3) - 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(5(-2sin(3πx - 1))^2 - 3(-2sin(3πx - 1)) + 2)^2 + 3(5(-2sin(3πx - 1))^2 - 3(-2sin(3πx - 1)) + 2) + 2 = 4((-3x + 2)/(-2x)) - 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) = (1(-2|(-3x^2 + 3x - 1) + 1|) - 1)/(-1(-2|(-3x^2 + 3x - 1) + 1|) - 2) and g(x) = 1(-2|x| + 2)^2 + 1(-2|x| + 2) - 1 where -10 ≤ x ≤ 10.

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


[User]
How many solutions does the equation 1(3|(-1x + 3) - 1| - 3)^2 - 4(3|(-1x + 3) - 1| - 3) - 3 = (-1(-2sin(2πx + 2) - 1) - 1)/(-1(-2sin(2πx + 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) = -2|(2(4x + 3) + 1) + 2| + 3 and g(x) = 2sin(3π(5x - 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) = 1cos(1π(-3|((-3x)/(1x - 3)) - 3|) - 3) - 1 and g(x) = -1|(-1sin(1πx - 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) = -4(1(-3x^2 + 5x + 1)^2 - 2(-3x^2 + 5x + 1) - 1)^2 + 1(1(-3x^2 + 5x + 1)^2 - 2(-3x^2 + 5x + 1) - 1) + 5 and g(x) = -1(-1e^(2x) + 3) + 1 intersect in the interval [-10, 10].

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


[User]
How many solutions does the equation 2sin(3π(1|(-4x^2 + 5x + 2)| - 1)) - 2 = -2|((-2x - 3)/(1x - 3)) + 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) = -3|((-2(-3|x + 1| + 2) + 2)/(1(-3|x + 1| + 2) + 3)) + 2| and g(x) = (-3(3cos(2πx + 2) - 2) + 2)/(1(3cos(2πx + 2) - 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) = 2e^(2((1(-1x - 1) - 1)/(-2(-1x - 1) + 3))) and g(x) = -4(3sin(3πx - 2) - 1)^2 + 5(3sin(3πx - 2) - 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) = (1(3cos(3π(1x) - 3) + 3) - 1)/(1(3cos(3π(1x) - 3) + 3) - 3) and g(x) = -3cos(1π(-2x + 3) + 2) - 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) = -4(2sin(3π((1x + 2)/(-2x + 1))) + 2)^2 + 5(2sin(3π((1x + 2)/(-2x + 1))) + 2) + 4 and g(x) = (-3(5x + 1) - 2)/(3(5x + 1) - 2) where -10 ≤ x ≤ 10.

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


[User]
How many solutions does the equation 4((-3(2x + 1) + 2)/(-3(2x + 1) - 1))^2 - 5((-3(2x + 1) + 2)/(-3(2x + 1) - 1)) + 3 = 3cos(2π(-1|x + 2| - 2) - 3) + 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(2π((2x + 3)/(2x)) + 1) - 3) - 1| + 1 and g(x) = 2cos(3π((-2x - 3)/(2x + 2)) + 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((-3(1x^2 + 4x + 3) - 2)/(-2(1x^2 + 4x + 3) + 1)) + 3 and g(x) = -1sin(2π(3x - 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) = 5(3(-1cos(3πx - 1) - 2)^2 - 1(-1cos(3πx - 1) - 2) - 5)^2 - 1(3(-1cos(3πx - 1) - 2)^2 - 1(-1cos(3πx - 1) - 2) - 5) + 1 and g(x) = 1(-2e^(-1x) - 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|(1(1x^2 - 2x + 1)^2 - 5(1x^2 - 2x + 1) + 4) - 3| and g(x) = 1|(1|x - 2| + 1) - 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) = 5(-2cos(3π(-2|x - 1| + 1)) + 1) - 5 and g(x) = 1(1cos(2πx) - 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) = 3|(4(-1sin(2πx + 2) + 1) - 5) + 2| - 2 and g(x) = -3((2x)/(-2x + 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((-1(-1|x + 2| - 2) - 1)/(1(-1|x + 2| - 2))) + 5 and g(x) = -3cos(3π(-3x^2 - 1x - 4) + 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) = -2(-1(-1e^(-1x) + 2) + 4) - 3 and g(x) = -5(1cos(2πx - 3) - 2)^2 + 2(1cos(2πx - 3) - 2) + 5 in the range -10 ≤ x ≤ 10?

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


[User]
How many solutions does the equation 2(-4(-5x^2 - 4x + 2)^2 + 2)^2 - 3(-4(-5x^2 - 4x + 2)^2 + 2) - 1 = (3(1|x + 3|) + 2)/(3(1|x + 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) = 1(3(2cos(1πx + 1) - 2)^2 - 3(2cos(1πx + 1) - 2) + 2)^2 - 4(3(2cos(1πx + 1) - 2)^2 - 3(2cos(1πx + 1) - 2) + 2) and g(x) = 3|(3e^(1x) + 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) = 3e^(-1((2(-1|x| + 2) - 3)/(-3(-1|x| + 2) - 2))) + 1 and g(x) = -1sin(2π(2x + 3) + 1) + 1 where -10 ≤ x ≤ 10.

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


[User]
How many solutions does the equation -1(-1(-1sin(3πx + 3) + 2) + 1)^2 + 4(-1(-1sin(3πx + 3) + 2) + 1) - 5 = -1(-1x - 5)^2 - 5(-1x - 5) + 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) = 2cos(2π(5(1x^2 + 4x + 1)^2 + 1) + 1) - 2 and g(x) = 3cos(2π(-2|x - 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) = -1sin(1π(5(-4x^2 + 3x - 4) + 2) + 2) - 1 and g(x) = -4(-5x^2 - 5x + 4) - 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) = 1|(1|(3x^2 + 1x - 2) - 2| - 3) + 3| - 3 and g(x) = -2|(3sin(2πx - 3)) - 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) = -1|(5(1x - 5)^2 + 5(1x - 5) - 4) - 1| + 3 and g(x) = (2(2x - 1) - 2)/(-2(2x - 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) = (-3(-2e^(1((-3x - 3)/(2x - 1))) + 1) - 2)/(2(-2e^(1((-3x - 3)/(2x - 1))) + 1) + 2) and g(x) = 3sin(1π(5x^2 - 5x - 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) = -1sin(3π((-3((1x + 3)/(1x - 2)) + 3)/(-2((1x + 3)/(1x - 2)))) + 2) and g(x) = (1(5x + 4) - 2)/(-1(5x + 4) + 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|(-3sin(3π(-5x^2 - 5x - 3) + 2) + 1)| + 2 and g(x) = 1|((-2x - 2)/(2x - 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) = (-2(-2((-1x + 2)/(-1x - 1))) - 3)/(2(-2((-1x + 2)/(-1x - 1))) + 1) and g(x) = 2cos(1π(-3|x - 3|) + 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(-2sin(2π(1x - 2) - 1) - 2) - 3)/(-3(-2sin(2π(1x - 2) - 1) - 2)) and g(x) = 4(2x + 4) - 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) = -5(5((-2x + 3)/(3x - 1))^2 + 2((-2x + 3)/(3x - 1)) + 5) + 5 and g(x) = (3(1cos(1πx - 1)) - 1)/(2(1cos(1πx - 1)) + 1) intersect in the interval [-10, 10].

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


[User]
How many solutions does the equation -1cos(2π(4(5x + 2)^2 - 2(5x + 2) - 2) - 1) + 1 = (-1(-5x^2 - 4x))/(-2(-5x^2 - 4x)) 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(1π(-1(4x^2 - 3x + 2)) + 1) + 2 and g(x) = (-1(-1e^(-1x) - 1) + 1)/(-1(-1e^(-1x) - 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) = (2((2(1|x + 2| - 3) + 1)/(1(1|x + 2| - 3))) + 2)/(-1((2(1|x + 2| - 3) + 1)/(1(1|x + 2| - 3)))) and g(x) = (2(4x^2 + 2x) - 3)/(2(4x^2 + 2x)) 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|(4(3sin(3πx - 1) - 3)^2 + 1(3sin(3πx - 1) - 3) - 4)| + 2 and g(x) = 4(-3x^2 + 3x + 2)^2 - 3(-3x^2 + 3x + 2) - 2 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((-3x - 3)/(-1x + 2)) + 3)/(-3((-3x - 3)/(-1x + 2)) + 4)) - 2) + 1 = -1(-3sin(1πx - 2) + 3)^2 + 4(-3sin(1πx - 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|(-1e^(2x) - 2) + 2| + 3)^2 + 1(-2|(-1e^(2x) - 2) + 2| + 3) - 2 = -3cos(3π((3x - 1)/(-3x)) - 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) = -1((2(3sin(2πx - 2) - 1))/(1(3sin(2πx - 2) - 1) + 1))^2 - 5((2(3sin(2πx - 2) - 1))/(1(3sin(2πx - 2) - 1) + 1)) + 1 and g(x) = -5(-1cos(2πx)) - 5 intersect in the interval [-10, 10].

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


[User]
How many solutions does the equation 2|(3|(1x^2 - 4x - 5) + 2| - 2) + 1| + 2 = 5(2sin(3πx + 3) - 1)^2 + 4(2sin(3πx + 3) - 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) = (-2(2cos(2π(2x + 2) + 1) + 1) + 3)/(1(2cos(2π(2x + 2) + 1) + 1) + 1) and g(x) = (-1(-3cos(1πx + 1) - 1) + 2)/(2(-3cos(1πx + 1) - 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) = -3(-4(-1x^2 + 2x + 1)^2 + 2(-1x^2 + 2x + 1) - 1)^2 - 3(-4(-1x^2 + 2x + 1)^2 + 2(-1x^2 + 2x + 1) - 1) + 5 and g(x) = (1(1|x| - 1) - 3)/(1(1|x| - 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) = (-1(4(-3e^(1x) + 2)^2 - 1(-3e^(1x) + 2)) + 1)/(-3(4(-3e^(1x) + 2)^2 - 1(-3e^(1x) + 2)) + 4) and g(x) = -5(-2sin(1πx + 3)) - 4 where -10 ≤ x ≤ 10.

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


[User]
How many solutions does the equation -2|(-4(-2sin(2πx) - 3) - 3) - 2| + 2 = 1|(2x^2 - 5x + 2) + 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((2(-1x - 4))/(-2(-1x - 4) - 2)) - 2)/(1((2(-1x - 4))/(-2(-1x - 4) - 2))) = -5(-1cos(1πx - 2) + 1)^2 - 5(-1cos(1πx - 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(-2|x - 3| + 3) - 5) + 3| - 1 and g(x) = 3(1|x + 2| - 3) - 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((2x + 1)/(2x + 3)) + 1)/(2((2x + 1)/(2x + 3)))))/(2((-1((2x + 1)/(2x + 3)) + 1)/(2((2x + 1)/(2x + 3))))) and g(x) = -2sin(3π(2x + 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(1((1x)/(-1x + 3)) + 2) + 2)/(3(1((1x)/(-1x + 3)) + 2) + 1) = -2|(3sin(2πx + 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) = -5(-2|(-3sin(3πx + 1) - 1)| + 3) and g(x) = (-1(-2|x - 3| + 1))/(-1(-2|x - 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 -1e^(1(3|(-2|x + 2| - 1) + 3| - 2)) + 2 = -1|(-2sin(1πx + 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) = (-2(4(-2cos(1πx - 2) - 2) + 4))/(1(4(-2cos(1πx - 2) - 2) + 4) + 3) and g(x) = 2(-1|x + 3| - 1) + 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) = 2cos(1π(-1|(2|x + 2| - 3) - 1| + 1) - 2) + 3 and g(x) = -3(-2cos(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) = -5((1(-3e^(-2x) + 3) + 2)/(-2(-3e^(-2x) + 3) - 3))^2 + 2((1(-3e^(-2x) + 3) + 2)/(-2(-3e^(-2x) + 3) - 3)) - 1 and g(x) = -1(-1x^2 + 4x + 3)^2 - 5(-1x^2 + 4x + 3) - 3 in the range -10 ≤ x ≤ 10?

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


[User]
How many solutions does the equation 1|(-1e^(-2(1x^2 + 4x)) - 3) + 2| = -2sin(1π(-1x^2 + 5x) + 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) = -2((2(-3sin(2πx) + 2) + 1)/(-2(-3sin(2πx) + 2) - 3))^2 + 5((2(-3sin(2πx) + 2) + 1)/(-2(-3sin(2πx) + 2) - 3)) + 1 and g(x) = 2|(-2cos(3πx - 2) + 2) - 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) = 1|(2(-3|x - 2| + 1)^2 + 2(-3|x - 2| + 1)) - 3| - 3 and g(x) = (-2(2sin(2πx - 3)) - 1)/(-3(2sin(2πx - 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) = -2(3sin(2π(-1|x - 3| - 3) + 1) + 3)^2 - 4(3sin(2π(-1|x - 3| - 3) + 1) + 3) + 4 and g(x) = -4(5x^2 + 2x + 4) - 4 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(-3cos(2π(-3x^2 - 5x + 2) + 1) + 2) - 4 and g(x) = 3e^(1(3x^2 - 5x - 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(3cos(3πx) - 2)^2 - 3(3cos(3πx) - 2) - 5) - 3)/(-3(1(3cos(3πx) - 2)^2 - 3(3cos(3πx) - 2) - 5) - 1) = -2e^(2(-2|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) = 3sin(3π((-1(-1|x + 2| - 2) + 2)/(-2(-1|x + 2| - 2) - 1)) - 2) - 2 and g(x) = 3sin(3π(-1x^2 - 4x - 5) - 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) = (3((3(2|x + 2| - 3) + 1)/(1(2|x + 2| - 3) - 2)) + 1)/(-1((3(2|x + 2| - 3) + 1)/(1(2|x + 2| - 3) - 2)) + 3) and g(x) = 3cos(1π(-5x^2 + 5x - 1) + 3) + 1 where -10 ≤ x ≤ 10.

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


[User]
How many solutions does the equation 3|(1|(3x + 3) - 2| - 3) + 1| - 2 = -1sin(1π(-1x^2 + 3x - 2) + 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 2|(-3(-1|x + 2| + 1) - 1) + 3| = (2(-2x + 1) + 3)/(3(-2x + 1) + 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((-1(2x - 5) + 1)/(-3(2x - 5) - 2)) + 3)/(2((-1(2x - 5) + 1)/(-3(2x - 5) - 2)) - 1) = -2|(-2sin(2πx + 3) - 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) = (-1(-3e^(-2((1x)/(-3x + 1))) + 3) - 2)/(-1(-3e^(-2((1x)/(-3x + 1))) + 3) - 2) and g(x) = -1sin(1π(1x^2 - 5x - 5) + 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(5(-2cos(1πx) - 2) - 5) + 4 and g(x) = 2|(-3x^2 - 1x) - 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) = 3cos(2π(5((-1x - 1)/(1x))^2 - 2((-1x - 1)/(1x)) - 1) - 3) - 1 and g(x) = (2(-3x + 2) + 1)/(1(-3x + 2) + 2) where -10 ≤ x ≤ 10.

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


[User]
How many solutions does the equation -3cos(1π(2|(-5x^2 + 4x - 2) - 2| + 3) - 3) - 1 = 1e^(-2(-4x - 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(1sin(2π(-1x + 5) - 2)))/(2(1sin(2π(-1x + 5) - 2)) + 1) and g(x) = 2sin(1π(-2|x - 3| + 2) - 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) = -2((3((2x + 2)/(3x + 1)))/(3((2x + 2)/(3x + 1)) - 2)) - 1 and g(x) = -1cos(3π(-4x - 4) + 1) - 2 in the range -10 ≤ x ≤ 10?

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


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

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


[User]
How many solutions does the equation -3(-2cos(1π(-3|x|) + 1) + 1)^2 + 1(-2cos(1π(-3|x|) + 1) + 1) - 4 = -2|((-2x + 3)/(2x - 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((2(-3|x + 3| - 2) + 2)/(1(-3|x + 3| - 2) - 3)) + 1)/(2((2(-3|x + 3| - 2) + 2)/(1(-3|x + 3| - 2) - 3)) + 3) and g(x) = (-1(-3sin(1πx + 1) + 1) - 1)/(2(-3sin(1πx + 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) = 1sin(2π(3|(1x^2 + 3x - 1) - 3| + 3) - 1) and g(x) = -3cos(1π((2x + 1)/(1x + 3)) + 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((3(-3|x - 3| - 3) + 3)/(2(-3|x - 3| - 3) - 3)) - 2 = 3cos(1π(5x^2 + 4x - 5) + 3) - 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(-2(-3x - 5)^2 - 5(-3x - 5) - 2) + 1 and g(x) = (2(-2cos(3πx) + 2) + 3)/(-3(-2cos(3πx) + 2)) intersect in the interval [-10, 10].

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


[User]
How many solutions does the equation -3sin(3π(-3|((-1x - 3)/(1x)) + 1| - 3) - 2) - 2 = -1|(1|x + 2| + 2) - 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) = -4(5(-1x + 2)^2 - 1)^2 - 5(5(-1x + 2)^2 - 1) - 3 and g(x) = 3cos(2π(2|x - 2| + 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|(1sin(2π(-2x^2 - 5x) - 2) - 3) + 1| - 1 and g(x) = -2|(-2cos(3πx) - 2) - 3| - 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) = -4(2sin(1π((-2x + 2)/(1x - 3)) + 2) + 1) + 2 and g(x) = -3sin(1π(-1x^2 - 4x - 2) + 1) + 3 where -10 ≤ x ≤ 10.

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


[User]
How many solutions does the equation -3cos(2π((2((3x + 2)/(2x - 1)) + 2)/(2((3x + 2)/(2x - 1)) - 1)) + 2) = -1cos(3π(-4x - 4) + 3) + 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(-4(-1sin(2πx + 2) - 2)^2 - 3(-1sin(2πx + 2) - 2) - 4)^2 + 1(-4(-1sin(2πx + 2) - 2)^2 - 3(-1sin(2πx + 2) - 2) - 4) - 4 and g(x) = -2|(3|x| + 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|(1(3sin(2πx - 2) - 2) + 2) - 2| and g(x) = 4((3x - 3)/(1x + 3)) - 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(-3|x + 1| + 3) + 3) - 1)/(2(-2(-3|x + 1| + 3) + 3) - 1) = (-2(5x^2 - 2x - 5) - 3)/(-3(5x^2 - 2x - 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) = 1cos(3π((-3((2x + 3)/(-2x + 1)) + 2)/(1((2x + 3)/(-2x + 1)) + 3)) - 2) - 1 and g(x) = 2sin(3π(-5x^2 + 1x - 5) - 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) = -1e^(-1(-3|(-3|x| + 1) + 3| - 2)) - 3 and g(x) = -2|(3cos(1πx) - 3)| - 3 where -10 ≤ x ≤ 10.

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


[User]
How many solutions does the equation 2(3(-2cos(1πx - 1) + 2)^2 + 5(-2cos(1πx - 1) + 2) - 1) + 2 = -3(-2x - 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) = (-1(-4(-1sin(1πx + 3) - 1) - 5) + 2)/(-3(-4(-1sin(1πx + 3) - 1) - 5) + 2) and g(x) = 3|(2x + 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) = (-3(-3sin(2π(2|x + 3| - 2) - 2) - 1))/(2(-3sin(2π(2|x + 3| - 2) - 2) - 1) + 1) and g(x) = -4(-1|x + 3| + 1)^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|(-2(2|x + 2| - 3) - 4) + 3| + 1 and g(x) = (-1(-4x^2 + 3x - 4) - 2)/(1(-4x^2 + 3x - 4) + 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|(-2x - 3) - 2| - 3) - 2)/(-1(-1|(-2x - 3) - 2| - 3)) and g(x) = -4(1sin(1πx - 2) - 1)^2 - 3(1sin(1πx - 2) - 1) + 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(-1(2sin(3πx - 1) + 1)^2 + 5(2sin(3πx - 1) + 1) + 2) and g(x) = 2|(3|x + 1| - 1) + 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(3cos(1π(-3x + 1) + 2) - 2))/(-3(3cos(1π(-3x + 1) + 2) - 2) - 2) and g(x) = -2|(-2x^2 - 4x - 2) + 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) = 1|(-2sin(3π(2x + 5) - 1) + 1) - 2| - 2 and g(x) = -5(-1x^2 - 4x - 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|(-2((3x + 1)/(-2x + 3))^2 - 1((3x + 1)/(-2x + 3)) - 3) + 1| - 1 and g(x) = 1(1cos(1πx) + 3)^2 - 4(1cos(1πx) + 3) - 3 where -10 ≤ x ≤ 10.

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


[User]
How many solutions does the equation (2(1|(-3sin(3πx) - 3) + 1| - 3) + 2)/(2(1|(-3sin(3πx) - 3) + 1| - 3) + 1) = -1(-1x^2 + 2x + 2)^2 - 5(-1x^2 + 2x + 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(2(-2x^2 - 1x + 2) + 5) - 2)/(-2(2(-2x^2 - 1x + 2) + 5) + 3) and g(x) = 2cos(3π(-4x^2 + 4x - 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 -4(2cos(3π(-1|x + 2| + 1) - 3) + 2)^2 - 4(2cos(3π(-1|x + 2| + 1) - 3) + 2) - 1 = -1|(3cos(1πx) + 2) + 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) = -2sin(2π(-4(2|x - 3|) - 5) - 1) + 1 and g(x) = 4((3x - 3)/(-3x - 1))^2 + 1((3x - 3)/(-3x - 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(-5(3cos(2πx + 3) + 2)^2 - 4(3cos(2πx + 3) + 2) + 3) + 5 and g(x) = 4(1x + 4)^2 + 3(1x + 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) = -5(2(3sin(2πx + 3) - 2) + 2)^2 + 2(2(3sin(2πx + 3) - 2) + 2) - 5 and g(x) = 3(-1|x| + 2) - 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|((2(4x - 5) + 2)/(-2(4x - 5))) - 2| - 3 and g(x) = 3(1sin(3πx - 3) + 3) - 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) = 2sin(2π(1(1x^2 - 3)^2 + 3(1x^2 - 3) - 2) - 3) - 1 and g(x) = 1((2x - 3)/(-3x + 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(-2x + 5) - 2)/(-3(-2x + 5) - 2)) + 3)/(1((-1(-2x + 5) - 2)/(-3(-2x + 5) - 2)) + 3) and g(x) = -2sin(1π(1|x - 1| + 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) = 2cos(2π(1(-1|x - 2| - 1)^2 + 1(-1|x - 2| - 1) + 2) - 3) - 1 and g(x) = -3|(-1|x - 2| + 3) + 1| where -10 ≤ x ≤ 10.

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


[User]
How many solutions does the equation 1e^(2(1|((3x + 2)/(-3x + 1)) + 1| - 2)) - 3 = 2cos(1π(1x^2 + 3x - 4) + 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(3|(3sin(3πx - 2) - 1) + 2| - 1))/(-2(3|(3sin(3πx - 2) - 1) + 2| - 1) + 1) and g(x) = 1sin(1π(3|x + 3| + 3) + 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(2|(-3sin(1πx + 2) + 3) + 2| - 3)^2 - 4(2|(-3sin(1πx + 2) + 3) + 2| - 3) + 1 and g(x) = -4(-1x - 4) - 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(3sin(2π(-3|x - 2| + 1) - 2) + 3) + 3)/(-1(3sin(2π(-3|x - 2| + 1) - 2) + 3) + 3) and g(x) = -1(1|x - 2| - 3) - 1 where -10 ≤ x ≤ 10.

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


[User]
How many solutions does the equation -3|(1cos(2π(-2|x - 2| - 3) - 1) - 3) - 1| = (2(2sin(3πx - 2) - 1) - 3)/(-2(2sin(3πx - 2) - 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|((3(2sin(2πx - 1) + 1) - 3)/(-2(2sin(2πx - 1) + 1) + 1)) - 3| and g(x) = 1|(-1x^2 + 3x) + 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) = -2|(2sin(1π((1x + 2)/(-2x + 3)) + 3) + 3) + 3| and g(x) = (-3(2sin(3πx - 3) - 1) + 3)/(1(2sin(3πx - 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(1sin(2π((-1x + 1)/(-2x + 3)) - 2) + 2) + 3)/(3(1sin(2π((-1x + 1)/(-2x + 3)) - 2) + 2) - 2) and g(x) = (-3(3x) - 1)/(-2(3x) + 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) = 3sin(1π(1|(-4x^2 - 3x) - 2| - 3) + 3) - 3 and g(x) = (3(-2e^(-1x) - 1) + 2)/(2(-2e^(-1x) - 1) + 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) = 2e^(-1((-3(-2x^2 + 2x - 1) - 3)/(1(-2x^2 + 2x - 1) + 2))) and g(x) = 4(-1cos(3πx) + 2)^2 - 5(-1cos(3πx) + 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((2(2|x + 1| - 1) - 3)/(-2(2|x + 1| - 1) - 1))^2 - 3((2(2|x + 1| - 1) - 3)/(-2(2|x + 1| - 1) - 1)) + 2 and g(x) = (1(3sin(3πx) + 1) + 2)/(2(3sin(3πx) + 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(-4(3cos(2πx + 2) - 2)^2 + 1(3cos(2πx + 2) - 2) - 3) + 1 and g(x) = 4(5x + 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) = 2(-1cos(2π(1x^2 - 3x - 1) + 2) + 3)^2 - 5(-1cos(2π(1x^2 - 3x - 1) + 2) + 3) - 1 and g(x) = 2|(-3x + 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 1cos(1π(-1(4x - 1)^2 + 4(4x - 1) + 3) + 2) + 3 = 2|(-2cos(2πx - 1) + 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 -3(-1((-1x + 1)/(-1x + 2)) - 1)^2 + 4(-1((-1x + 1)/(-1x + 2)) - 1) + 5 = -3(2x^2 + 5x - 1)^2 - 3(2x^2 + 5x - 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) = (-2((-2(1x^2 + 2x + 5) + 3)/(1(1x^2 + 2x + 5))))/(-2((-2(1x^2 + 2x + 5) + 3)/(1(1x^2 + 2x + 5))) + 3) and g(x) = -2cos(1π(-1x - 2) - 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((1(-3sin(1πx - 2) - 2) + 3)/(1(-3sin(1πx - 2) - 2))) - 4 and g(x) = -2cos(2π(-2x^2 + 2x - 4) - 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((1(-1x^2 + 3x) - 3)/(-1(-1x^2 + 3x) + 2)) + 3) + 2 and g(x) = (-1(3|x + 2| + 1) + 1)/(-2(3|x + 2| + 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) = 5(1((-2x - 1)/(-1x)) - 2)^2 - 1(1((-2x - 1)/(-1x)) - 2) - 1 and g(x) = 2sin(1π(5x^2 + 1x + 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 1((-3(-3cos(3πx + 3)) - 3)/(-2(-3cos(3πx + 3)) - 1))^2 - 3((-3(-3cos(3πx + 3)) - 3)/(-2(-3cos(3πx + 3)) - 1)) - 1 = 5(1e^(1x) + 2)^2 - 2(1e^(1x) + 2) + 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(-3sin(2π(-2|x - 3| - 2) + 2) + 1) + 2)/(-1(-3sin(2π(-2|x - 3| - 2) + 2) + 1)) and g(x) = 1sin(3π(3|x - 1| - 1) - 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(-1(3cos(1πx - 1) - 1)^2 - 4(3cos(1πx - 1) - 1) + 1) + 2)/(-1(-1(3cos(1πx - 1) - 1)^2 - 4(3cos(1πx - 1) - 1) + 1) - 2) and g(x) = -3(-2e^(1x) - 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(3sin(1π(-2|x - 2|) - 3) + 1) + 5 and g(x) = (-1((1x)/(3x - 2)) - 2)/(1((1x)/(3x - 2)) - 2) intersect in the interval [-10, 10].

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


[User]
How many solutions does the equation 3|((2((1x + 2)/(-2x + 1)) + 3)/(-3((1x + 2)/(-2x + 1)) + 2))| + 2 = -3sin(1π(-5x^2 - 3x + 5) - 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(3π((3(3x^2 - 1x - 3) - 1)/(-1(3x^2 - 1x - 3))) - 2) and g(x) = 2sin(3π(3|x + 3| - 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 4(2(-1|x - 2| + 3) + 2)^2 + 3(2(-1|x - 2| + 3) + 2) - 5 = -3((2x - 3)/(-2x + 1)) - 5 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(3cos(3π(2x^2 - 1x) - 1) - 1) - 1 and g(x) = 5(-1|x| + 2)^2 - 1(-1|x| + 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((3(3|x + 1| + 3) - 2)/(3(3|x + 1| + 3))) - 3)/(-1((3(3|x + 1| + 3) - 2)/(3(3|x + 1| + 3))) - 1) and g(x) = 1(-3cos(3πx - 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) = 3cos(1π(2(2x^2)) - 2) - 1 and g(x) = 2sin(3π(1|x + 1| + 1) + 1) - 1 intersect in the interval [-10, 10].

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


[User]
How many solutions does the equation (-1(1|(3sin(2πx) + 1) - 1| - 2) + 3)/(1(1|(3sin(2πx) + 1) - 1| - 2) + 1) = 1|(-1x^2 - 1) + 1| - 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|(-3cos(3π(-4x^2 + 5x) - 1) + 1) - 2| - 3 = (-2(-3x + 1) + 2)/(1(-3x + 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) = 2e^(1(-3(1|x - 3| + 3)^2 - 3(1|x - 3| + 3) - 5)) + 2 and g(x) = 2cos(3π(-4x^2 + 1x + 4)) + 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((-1(-2x^2 + 5x + 4) + 1)/(-2(-2x^2 + 5x + 4) - 1))^2 + 5((-1(-2x^2 + 5x + 4) + 1)/(-2(-2x^2 + 5x + 4) - 1)) - 3 and g(x) = -3(2x^2 - 3x + 3) + 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(2π(-1|(-2|x + 2| + 3) - 3|) - 3) and g(x) = 1e^(2((2x + 2)/(-1x + 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(2x^2 - 2x - 1)))^2 - 4(2cos(2π(2x^2 - 2x - 1))) + 2 = 1cos(2π(1x + 4) + 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 -2cos(2π(-2|(5x)| + 3) + 3) = 2sin(2π(1|x + 2| + 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(-2sin(1π(2|x + 3| - 3) + 3)) - 4 and g(x) = -3(1sin(2πx) + 2)^2 + 2(1sin(2πx) + 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|((-1(-3sin(3πx - 3) - 2) + 3)/(-1(-3sin(3πx - 3) - 2) - 2))| - 2 and g(x) = -2(-2cos(2πx + 1) - 3)^2 - 3(-2cos(2πx + 1) - 3) + 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) = 1(2|(-3e^(-1x) - 3) + 2| - 3)^2 - 5(2|(-3e^(-1x) - 3) + 2| - 3) + 4 and g(x) = -3cos(3π(-2x + 5) + 1) - 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((-1(1x^2 - 1x - 3) + 2)/(-3(1x^2 - 1x - 3))) - 1)/(-2((-1(1x^2 - 1x - 3) + 2)/(-3(1x^2 - 1x - 3))) - 3) and g(x) = (-2(3x^2 - 2x + 1) + 3)/(2(3x^2 - 2x + 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) = -4(5(-3x^2 + 4x - 1)^2 + 1(-3x^2 + 4x - 1) - 3)^2 + 5(5(-3x^2 + 4x - 1)^2 + 1(-3x^2 + 4x - 1) - 3) - 2 and g(x) = 1((2x + 3)/(3x - 2)) - 5 where -10 ≤ x ≤ 10.

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


[User]
How many solutions does the equation -3sin(3π(-2((-3x - 2)/(1x + 3))^2 - 4((-3x - 2)/(1x + 3)) - 4) - 3) + 2 = (3(-2|x - 1| + 2))/(2(-2|x - 1| + 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(-2cos(1π(2|x - 1| + 1)) + 1) - 1)/(1(-2cos(1π(2|x - 1| + 1)) + 1) - 3) and g(x) = (2((1x - 1)/(-3x + 1)) + 1)/(2((1x - 1)/(-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(-5(-1x^2 - 3x) + 2)^2 - 2(-5(-1x^2 - 3x) + 2) + 5 = -3(3cos(3πx) + 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(-1e^(-1x) + 1)) - 4 and g(x) = 1(-1cos(1πx - 1) + 3)^2 + 3(-1cos(1πx - 1) + 3) - 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) = 4((2(1x^2 + 1x - 4) - 1)/(-2(1x^2 + 1x - 4))) + 5 and g(x) = -3|(-3x - 4)| + 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) = -5(2sin(3π(-1|x|) - 2) - 3)^2 - 2 and g(x) = -5(-3cos(2πx) + 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) = -2cos(1π(5((-1x - 3)/(2x + 2))^2 - 5((-1x - 3)/(2x + 2)) + 2) - 3) - 3 and g(x) = -2|(-1cos(1πx + 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) = 3(1(2|x + 1| - 2)^2 - 1(2|x + 1| - 2) - 2) + 5 and g(x) = -1sin(1π(-5x - 5) - 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) = (1(2cos(2π(1x) - 3) + 2) - 1)/(-1(2cos(2π(1x) - 3) + 2)) and g(x) = 4(-1|x| + 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) = (2(2|(-4x - 2) - 3| + 2) - 3)/(2(2|(-4x - 2) - 3| + 2) + 2) and g(x) = 1(4x^2 + 2x - 5)^2 + 3(4x^2 + 2x - 5) + 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|(-5(1x^2 - 5x + 1))| - 3 and g(x) = (3(2e^(2x) + 3) - 2)/(2(2e^(2x) + 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|(4(1x^2 - 1x - 1) + 1) - 2| - 2 and g(x) = (3(-2e^(1x) - 2))/(1(-2e^(1x) - 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) = -1cos(2π((-3(3x + 1) - 3)/(-2(3x + 1) + 3))) + 1 and g(x) = 1(-2x^2 - 1x - 5)^2 + 5(-2x^2 - 1x - 5) + 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|(-2sin(1π(3x^2 + 4x - 5) + 1) + 2) + 1| + 3 and g(x) = 1(-4x - 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) = 3((1(-2|x + 2| + 3) + 2)/(1(-2|x + 2| + 3) + 1)) - 2 and g(x) = -3(-3cos(1πx - 3) + 2)^2 - 4(-3cos(1πx - 3) + 2) + 4 in the range -10 ≤ x ≤ 10?

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


[User]
How many solutions does the equation 1|(3sin(1π((-2x + 3)/(-3x - 1)) + 3) - 1) - 3| - 3 = -2cos(1π(-3x^2 - 5x + 2) - 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) = 1sin(2π(4(3|x + 1| - 3)^2 + 1(3|x + 1| - 3) + 1) - 3) - 1 and g(x) = (3(-5x^2 - 2x + 1) + 2)/(3(-5x^2 - 2x + 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(2cos(2π(-1|x|) - 3) + 1)^2 + 3 and g(x) = -1((3x + 3)/(-2x - 1))^2 - 1((3x + 3)/(-2x - 1)) + 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(5((-3x - 3)/(1x - 2))^2 + 3((-3x - 3)/(1x - 2)))) - 1 and g(x) = (-1(1|x + 1| - 1) - 3)/(3(1|x + 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) = -2sin(1π((-3(-1|x| - 2) - 3)/(-1(-1|x| - 2) - 3))) + 1 and g(x) = -2cos(1π((1x - 2)/(-3x - 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) = 1sin(1π((1(2x^2 - 4x - 1) - 1)/(1(2x^2 - 4x - 1) + 3)) + 3) + 1 and g(x) = -1(-4x^2 + 2x + 4) - 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((-3(4x) + 2)/(-1(4x) + 2)) - 5 and g(x) = -3|(-3|x + 2| + 3) - 1| + 1 in the range -10 ≤ x ≤ 10?

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


[User]
How many solutions does the equation -3(3e^(1(-1x^2 - 4x - 1)) - 3)^2 + 4(3e^(1(-1x^2 - 4x - 1)) - 3) - 2 = 1sin(3π((-1x - 1)/(3x + 3)) + 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(-4((3x - 3)/(-1x))^2 + 5((3x - 3)/(-1x))) + 2)/(-3(-4((3x - 3)/(-1x))^2 + 5((3x - 3)/(-1x))) - 2) and g(x) = -3sin(2π(-4x + 2) + 3) - 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(3π(-3(-3|x + 1| - 2) + 5) + 3) - 3 and g(x) = 2cos(3π((2x + 2)/(-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) = -5(3(1e^(-1x)) - 2)^2 + 1(3(1e^(-1x)) - 2) - 2 and g(x) = -2|((3x + 1)/(-1x - 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) = (-2(2sin(1π(-2x^2 - 2x - 5) + 2)) - 2)/(-1(2sin(1π(-2x^2 - 2x - 5) + 2)) - 3) and g(x) = 2e^(-2(2|x + 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) = 1(5(-2|x + 2| + 2)^2 - 4(-2|x + 2| + 2))^2 + 1(5(-2|x + 2| + 2)^2 - 4(-2|x + 2| + 2)) + 5 and g(x) = 5(2|x + 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) = -2cos(3π(1((-2x - 1)/(-1x - 2)) - 5)) - 1 and g(x) = -1|(-1|x - 2| + 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) = -1(1|(-2cos(1πx - 1) - 2) + 3| - 3)^2 + 4(1|(-2cos(1πx - 1) - 2) + 3| - 3) + 3 and g(x) = (2(2sin(2πx + 1) - 2) + 3)/(2(2sin(2πx + 1) - 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) = 2sin(1π(-3|(-3|x + 2|)| - 2) - 1) + 2 and g(x) = (1(-2|x - 3| + 1) + 2)/(1(-2|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) = 2cos(3π(-5(3x^2 + 5x) + 5) - 3) + 2 and g(x) = 3|(-2cos(3πx + 2) - 1) + 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(-1e^(-2(1x^2 + 5)) - 1) - 1 and g(x) = -3(1cos(1πx - 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((-2x - 3)/(-2x)) + 2)/(-2((-2x - 3)/(-2x)) - 1)) + 1 = (3(3sin(2πx - 3)) - 3)/(3(3sin(2πx - 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(2e^(-1(-1|x + 2|)) - 3) - 5 and g(x) = 2(3sin(2πx) - 3)^2 + 3(3sin(2πx) - 3) + 1 in the range -10 ≤ x ≤ 10?

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


[User]
How many solutions does the equation -3sin(3π(-4(-5x + 4)^2 + 1) - 2) + 3 = 2(-1sin(2πx + 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) = -1(-4(-1sin(2πx) - 3)^2 - 1(-1sin(2πx) - 3) - 5)^2 - 3(-4(-1sin(2πx) - 3)^2 - 1(-1sin(2πx) - 3) - 5) + 3 and g(x) = -5(3|x + 1| + 2)^2 - 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(-3(-2x - 4) - 2)^2 and g(x) = 2cos(3π((-2x)/(2x + 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|(-3|x + 2| - 1) + 3| + 3) + 2 and g(x) = (1(-2cos(2πx + 3) + 2) + 2)/(1(-2cos(2πx + 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) = -1sin(2π(-5(1|x - 2| - 3)^2 - 4(1|x - 2| - 3) + 5) + 2) + 2 and g(x) = 1e^(2(3x)) + 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) = 3sin(2π(-1|(-3x - 2) - 3| - 2)) + 1 and g(x) = -2cos(2π(1|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 3|(1cos(1π((-2x + 2)/(1x + 1)) + 1) + 3) - 3| - 2 = -3(3x + 5)^2 + 1(3x + 5) + 5 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(-4(-1e^(1x) + 2) - 2) + 1)/(2(-4(-1e^(1x) + 2) - 2) - 3) and g(x) = -1(1sin(2πx + 3) - 3)^2 - 2(1sin(2πx + 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) = -2cos(3π(2(2x + 5)^2 + 1(2x + 5) - 5) + 2) + 1 and g(x) = 1cos(2π(1x^2 + 3x + 5) - 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) = -1cos(2π((-1(-3x) + 2)/(-2(-3x) - 2)) - 3) and g(x) = 2cos(1π(-2|x - 3| - 2) - 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) = -3(4(4x^2 - 5x - 3)^2 - 5)^2 + 1(4(4x^2 - 5x - 3)^2 - 5) - 1 and g(x) = -1|(-1sin(2πx - 3) - 2) - 2| - 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) = 4(3sin(3π(4x^2 - 2x + 5)) + 2)^2 - 1(3sin(3π(4x^2 - 2x + 5)) + 2) + 3 and g(x) = 3|(-1|x - 1| - 1) - 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(2cos(3πx + 1)) + 3)/(-3(2cos(3πx + 1)) + 2)) + 2 and g(x) = 2cos(2π(-2x^2 + 3x + 1) - 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) = -1(1cos(1π(-2|x - 3|) - 3) + 1)^2 - 3(1cos(1π(-2|x - 3|) - 3) + 1) + 5 and g(x) = 2cos(3π((-3x + 3)/(-1x - 2)) + 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) = 3((-1(5x^2 - 4x - 1) - 1)/(3(5x^2 - 4x - 1) + 1))^2 + 4((-1(5x^2 - 4x - 1) - 1)/(3(5x^2 - 4x - 1) + 1)) + 1 and g(x) = -2((-2x)/(3x + 2))^2 + 1((-2x)/(3x + 2)) + 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|(-3(-1e^(-2x) + 1) + 2) - 2| and g(x) = (-1(2sin(2πx - 1) + 2) + 1)/(2(2sin(2πx - 1) + 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) = 3cos(3π(-3|(-1x + 4) - 1| + 3) + 2) and g(x) = (-3(-4x + 1) + 1)/(3(-4x + 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((-2(-3cos(1πx + 1) - 2) - 2)/(-3(-3cos(1πx + 1) - 2) - 1))^2 + 5((-2(-3cos(1πx + 1) - 2) - 2)/(-3(-3cos(1πx + 1) - 2) - 1)) + 4 and g(x) = -1((2x - 3)/(-2x)) + 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) = -1(-1(2e^(-2x) - 3)^2 - 2(2e^(-2x) - 3) + 2) + 5 and g(x) = 2sin(1π(-5x + 4) - 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) = -3e^(-1(5(1x - 5)^2 - 3(1x - 5) - 3)) - 2 and g(x) = -4(2e^(-1x) - 3)^2 + 4(2e^(-1x) - 3) + 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) = 2((-3(-3sin(1πx - 2) - 3) + 1)/(2(-3sin(1πx - 2) - 3) - 3))^2 - 3((-3(-3sin(1πx - 2) - 3) + 1)/(2(-3sin(1πx - 2) - 3) - 3)) and g(x) = 2|(-2x + 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) = -1cos(2π(-2|(1|x + 3|) + 2| - 3) - 3) - 3 and g(x) = 1((1x - 1)/(1x - 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) = -3sin(1π((-2((1x - 3)/(-1x + 2)) + 3)/(2((1x - 3)/(-1x + 2)) + 2)) + 1) and g(x) = -1|(4x + 5)| + 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(-1e^(2(1x^2 - 3x - 3)) + 3)^2 + 5(-1e^(2(1x^2 - 3x - 3)) + 3) + 1 and g(x) = -2((-3x + 1)/(1x + 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) = -3sin(1π((1((-1x + 1)/(1x - 3)) + 3)/(3((-1x + 1)/(1x - 3)) + 2)) - 1) - 1 and g(x) = (-3((-2x - 1)/(-3x + 1)))/(-1((-2x - 1)/(-3x + 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|(4(-1x^2 + 3x + 1)^2 - 1(-1x^2 + 3x + 1) - 4) + 1| + 1 and g(x) = -3|(5x^2 - 5x - 4) - 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|((1(-2cos(1πx - 1)) + 3)/(2(-2cos(1πx - 1)) + 3)) - 1| and g(x) = 3|(1x^2 - 5x)| - 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) = 4(1|(3cos(2πx) + 3) - 1| - 3) + 2 and g(x) = 3(-2x - 2)^2 + 4(-2x - 2) - 5 where -10 ≤ x ≤ 10.

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


[User]
How many solutions does the equation -2|(-2|(3sin(2πx) + 3) - 3| + 2) - 3| = 5(-3|x + 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(-4(-3x - 3) - 3) - 2) + 3 and g(x) = -3(2|x + 1|)^2 + 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) = -3sin(1π((-2((-3x + 3)/(-3x - 3)) - 2)/(-2((-3x + 3)/(-3x - 3)) - 3)) + 2) + 1 and g(x) = (-3(2|x + 3| - 3) + 1)/(3(2|x + 3| - 3) + 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(-2cos(2π(1x^2 + 1x + 3) + 1) - 2)^2 + 3(-2cos(2π(1x^2 + 1x + 3) + 1) - 2) + 4 and g(x) = (1(2|x - 3| - 3) - 2)/(1(2|x - 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(-1cos(1π(-4x^2 - 4x + 4) + 1) - 2))/(3(-1cos(1π(-4x^2 - 4x + 4) + 1) - 2) - 2) and g(x) = 2cos(1π(1x - 4) + 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) = -1(-3(-4x^2 + 4x + 3)^2 + 2(-4x^2 + 4x + 3) - 2)^2 + 3(-3(-4x^2 + 4x + 3)^2 + 2(-4x^2 + 4x + 3) - 2) - 4 and g(x) = -3e^(-1(-3|x + 1| - 1)) - 1 where -10 ≤ x ≤ 10.

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


[User]
How many solutions does the equation (-3(3sin(3π(-3x^2 + 2x) - 1) + 3) - 3)/(-2(3sin(3π(-3x^2 + 2x) - 1) + 3) + 3) = -2((-3x - 1)/(-3x - 1))^2 - 3((-3x - 1)/(-3x - 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(2(-3sin(1πx - 3))^2 + 4(-3sin(1πx - 3)) + 4) + 5 and g(x) = 3(3cos(3πx - 3) - 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) = (-2(-5((1x - 1)/(-2x + 1)) + 5) + 2)/(1(-5((1x - 1)/(-2x + 1)) + 5) + 2) and g(x) = 3sin(1π(-1x) - 3) - 3 in the range -10 ≤ x ≤ 10?

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


[User]
How many solutions does the equation (1(3e^(2(-1x^2 - 5x + 5)) + 1) - 2)/(-3(3e^(2(-1x^2 - 5x + 5)) + 1) - 2) = 1|(2sin(1πx + 3) - 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) = 4(1|(-2sin(3πx - 1) - 1) - 1| - 3) and g(x) = 1(-3x - 4) + 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(1π(-2|((2x - 2)/(1x - 3))| - 1) + 1) + 2 and g(x) = 2sin(3π(-1|x + 2| + 3) + 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) = 2cos(2π((2((-2x + 3)/(-1x + 3)) - 1)/(2((-2x + 3)/(-1x + 3)) + 1)) - 1) + 2 and g(x) = 2sin(3π(3x^2 + 2x + 4) - 3) + 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) = -1e^(-1((1(-4x + 5) + 1)/(2(-4x + 5)))) - 2 and g(x) = -2|(-3x^2 - 1x + 2) + 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((2x + 1)/(3x + 1))^2 - 4((2x + 1)/(3x + 1)) + 1) - 1 = 1sin(3π(1x^2 - 5) - 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) = -1(-3sin(2π(-1|x + 2|) - 3) + 2) + 5 and g(x) = -1sin(1π((-2x - 1)/(3x - 1)) + 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) = 4(1((-1x + 2)/(-2x + 1))^2 - 3((-1x + 2)/(-2x + 1)) - 5)^2 + 5(1((-1x + 2)/(-2x + 1))^2 - 3((-1x + 2)/(-2x + 1)) - 5) - 3 and g(x) = (-1(-1|x + 2| + 2) + 1)/(-1(-1|x + 2| + 2) + 3) intersect in the interval [-10, 10].

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


[User]
How many solutions does the equation (-2(1|(-2x) + 2| - 2) - 2)/(2(1|(-2x) + 2| - 2) - 1) = 1sin(2π(2|x + 3| + 3) - 1) - 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(-1sin(2π(3x - 5) + 2) + 3) - 3)/(3(-1sin(2π(3x - 5) + 2) + 3) - 2) = -4(-2cos(3πx - 1) + 3)^2 + 5(-2cos(3πx - 1) + 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 -1(2sin(1π((-2x + 3)/(-1x)) + 1) + 3) + 5 = 1(4x^2 + 2x + 5)^2 - 4(4x^2 + 2x + 5) 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(-4(-3x^2 + 5x - 5) + 4)) - 3 and g(x) = -2e^(2(-2|x + 1| - 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) = -2|(3(1x^2 - 5x + 4) + 2) + 3| - 2 and g(x) = (3((-1x - 3)/(3x + 1)) - 2)/(-2((-1x - 3)/(3x + 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(2cos(2π((3x + 1)/(-2x + 3)) - 1) + 1)^2 - 1(2cos(2π((3x + 1)/(-2x + 3)) - 1) + 1) - 2 and g(x) = 5(-1|x + 3| + 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(-3e^(1(1|x - 1| - 2)) + 1) - 2)/(-1(-3e^(1(1|x - 1| - 2)) + 1) + 2) = -4(1x^2 - 2x - 4)^2 - 2(1x^2 - 2x - 4) + 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(-2sin(3π(-2|x - 3|) + 2) - 2)^2 - 2(-2sin(3π(-2|x - 3|) + 2) - 2) - 2 = (-1(-1x^2 - 3x - 1) + 2)/(-3(-1x^2 - 3x - 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 1|(3|(-5x^2 + 2x + 1) + 1| + 2)| + 2 = 4(-1cos(2πx) - 3)^2 + 4(-1cos(2πx) - 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(-2cos(3π(3x + 2)) + 2) and g(x) = 1sin(3π((-1x + 1)/(-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) = (2(-2((1x + 2)/(2x - 1))^2 + 2((1x + 2)/(2x - 1)) - 2) - 2)/(-2(-2((1x + 2)/(2x - 1))^2 + 2((1x + 2)/(2x - 1)) - 2) + 3) and g(x) = -3sin(1π(-4x - 4) + 1) in the range -10 ≤ x ≤ 10?

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


[User]
How many solutions does the equation -1|(2cos(2π((-2x - 3)/(-1x)) + 2) + 3) - 1| + 2 = 3|(-2x^2 - 5x + 3) + 2| - 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(2(-1e^(-1x))^2 + 2(-1e^(-1x)))^2 - 3(2(-1e^(-1x))^2 + 2(-1e^(-1x))) and g(x) = -4(-3sin(2πx - 1) + 1)^2 - 3(-3sin(2πx - 1) + 1) + 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) = 2sin(2π(3(-4x^2 - 1)^2 + 5(-4x^2 - 1) - 4) + 1) - 2 and g(x) = (-1(1|x|) - 3)/(-3(1|x|) + 4) in the range -10 ≤ x ≤ 10?

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


[User]
How many solutions does the equation 5((3(1x^2 - 1x - 1) - 2)/(3(1x^2 - 1x - 1) + 3)) - 5 = 2cos(1π(4x^2 + 3x + 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) = -1(4(-2cos(2πx + 1) + 1) + 4) + 4 and g(x) = 2e^(2((1x + 2)/(-2x - 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) = -5(-2|(-3cos(3πx + 2) + 2) - 2| - 3) - 5 and g(x) = -1(-3x + 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(3sin(3π(-4x^2 + 5x + 3) + 2) - 2) - 2)/(-2(3sin(3π(-4x^2 + 5x + 3) + 2) - 2) + 1) and g(x) = -5((2x + 3)/(2x + 2))^2 + 1((2x + 3)/(2x + 2)) + 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(4(1x^2 + 5x)^2 - 3(1x^2 + 5x) - 5) + 1)/(1(4(1x^2 + 5x)^2 - 3(1x^2 + 5x) - 5) - 3) and g(x) = (-2(-4x + 4))/(1(-4x + 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) = 2(3|(-1sin(1πx + 1) - 1) - 1| - 2)^2 + 3(3|(-1sin(1πx + 1) - 1) - 1| - 2) + 5 and g(x) = 1|(2x^2 + 4x - 5) - 3| in the range -10 ≤ x ≤ 10?

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


[User]
How many solutions does the equation -3|((3(1x^2 + 3x + 1) - 1)/(-2(1x^2 + 3x + 1) - 1))| - 2 = 2(-1sin(3πx + 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(-1cos(3π(4x^2 + 3) + 2) - 1) and g(x) = -3(-2sin(3πx + 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) = -1((-2(-2x^2 + 5) - 1)/(3(-2x^2 + 5) - 2))^2 + 2((-2(-2x^2 + 5) - 1)/(3(-2x^2 + 5) - 2)) + 3 and g(x) = 1(2x - 4) + 4 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(-3e^(-2(-1|x + 1| + 1)) + 2) + 1)/(2(-3e^(-2(-1|x + 1| + 1)) + 2) + 3) and g(x) = 3(-2sin(2πx - 1) - 2)^2 + 1(-2sin(2πx - 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) = -1sin(2π(-2|(4x^2 + 2x - 1) - 2| + 3) - 3) - 2 and g(x) = -1((1x - 3)/(2x + 1))^2 + 3((1x - 3)/(2x + 1)) - 4 in the range -10 ≤ x ≤ 10?

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


[User]
How many solutions does the equation 3(2sin(1π(3|x - 1| - 3) + 2) - 1) = 5((-1x + 2)/(-1x))^2 - 2((-1x + 2)/(-1x)) - 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) = 3|(-1(1e^(2x))) + 1| - 3 and g(x) = (-1(-2cos(2πx - 3)) - 2)/(-3(-2cos(2πx - 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) = -1|(-5(3sin(3πx + 3) + 3) - 2) + 2| + 1 and g(x) = 1|(-2e^(2x)) - 1| - 2 intersect in the interval [-10, 10].

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


[User]
How many solutions does the equation (-3(3sin(1π(2x - 1) - 2) - 1) - 1)/(3(3sin(1π(2x - 1) - 2) - 1) + 2) = (1(-3sin(1πx + 1) + 3) - 3)/(-3(-3sin(1πx + 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 -2|(2((-3x + 2)/(-1x - 3)) - 5) - 1| = -5(-3|x + 2| + 3)^2 - 5(-3|x + 2| + 3) + 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) = (1(1cos(1π(4x - 4)) - 1) + 3)/(1(1cos(1π(4x - 4)) - 1) - 2) and g(x) = (2(-3cos(1πx) + 1) + 2)/(3(-3cos(1πx) + 1) + 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) = 2sin(3π(-2|(3x^2 + 3x + 1) - 3| - 1)) and g(x) = -3e^(2(4x - 5)) + 1 in the range -10 ≤ x ≤ 10?

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


[User]
How many solutions does the equation (-1(-3sin(1π(-4x^2 - 2x + 2) + 1) - 3) - 3)/(2(-3sin(1π(-4x^2 - 2x + 2) + 1) - 3) + 1) = (-2(-1x^2 + 4x - 1) - 3)/(-2(-1x^2 + 4x - 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(2sin(1π(-1x - 1)) - 1)^2 + 4(2sin(1π(-1x - 1)) - 1) + 4 and g(x) = 2|((1x + 2)/(-1x + 3))| - 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) = 3(-3sin(1π(-1|x - 2| + 2) + 2) + 3) - 4 and g(x) = 3sin(2π(1|x| + 1) - 3) - 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(1sin(1πx) - 1) + 2)^2 + 5 and g(x) = -5(-2cos(1πx - 1))^2 - 5(-2cos(1πx - 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) = 4(-2|(-1x^2 + 4x) + 1| - 1) - 3 and g(x) = -3|(3cos(2πx + 2) + 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(3|(2|x + 1| + 3) + 3| - 1) - 3)/(3(3|(2|x + 1| + 3) + 3| - 1) - 2) and g(x) = -2sin(3π(-3x^2 - 1) + 2) - 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) = 2sin(3π(-1(1x - 5) + 4)) - 3 and g(x) = 2cos(3π(-3|x - 2| + 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) = -3|(3sin(2π((1x + 1)/(2x + 3)) + 1) + 2)| - 2 and g(x) = -3|(-2x + 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) = -2|((3(2sin(2πx - 2) + 3) - 2)/(-2(2sin(2πx - 2) + 3))) + 2| + 3 and g(x) = 2cos(2π(3|x| + 1) + 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) = (3(3cos(1π((1x - 1)/(-1x + 2)) - 2) + 1) - 3)/(2(3cos(1π((1x - 1)/(-1x + 2)) - 2) + 1) - 1) and g(x) = -2sin(2π(4x^2 + 4) - 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) = 3(-1|(5x + 3)| - 2) + 3 and g(x) = -1|(2x^2 + 1x + 1) + 2| - 3 where -10 ≤ x ≤ 10.

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


[User]
How many solutions does the equation (-1(-2cos(2π(-2x^2 - 4x + 1) + 3) - 3) + 2)/(-3(-2cos(2π(-2x^2 - 4x + 1) + 3) - 3) - 3) = (3(-2|x + 2|))/(-2(-2|x + 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) = 1|(2sin(1π(1x^2 - 2x) - 1) + 3) - 3| and g(x) = 5(2sin(2πx)) 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) = -2e^(-1((1(-1x + 3) - 3)/(1(-1x + 3) - 2))) - 1 and g(x) = -2sin(2π(-2|x + 3| - 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 3sin(3π((-2((-1x + 3)/(-2x)) + 1)/(-1((-1x + 3)/(-2x)) - 3)) - 3) - 1 = -2sin(3π(-1x^2 - 1x - 4) - 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 2e^(-2((-3(-1|x - 1| + 3) + 1)/(-2(-1|x - 1| + 3) - 2))) + 2 = -2|(-1sin(1πx + 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|((-1((1x + 3)/(2x + 1)) - 1)/(-1((1x + 3)/(2x + 1)) - 1)) - 2| - 1 = 2sin(2π(1|x - 1| - 2) + 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(1π(-3((-3x - 1)/(1x + 1))^2 + 4((-3x - 1)/(1x + 1)) - 5) + 1) + 2 and g(x) = -5((-2x + 3)/(2x)) - 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(3|(-1x - 4)| - 2) - 1)/(-1(3|(-1x - 4)| - 2)) and g(x) = 1|((1x + 3)/(1x)) - 3| - 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) = 3((3(-2x + 1) + 3)/(-2(-2x + 1))) + 4 and g(x) = -1(-2cos(1πx + 1))^2 - 4(-2cos(1πx + 1)) + 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) = (-1(2e^(1(3x)) + 2) - 2)/(-3(2e^(1(3x)) + 2)) and g(x) = 3|(-1x^2 - 5x + 4) + 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) = -2cos(1π(4((2x - 2)/(1x))^2 + 3((2x - 2)/(1x)) - 2)) and g(x) = (2(-5x^2 + 1x + 2) + 3)/(-3(-5x^2 + 1x + 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((-1(1|x| - 2) + 2)/(3(1|x| - 2) - 2)) + 4 = -1(-5x^2 + 5)^2 + 5(-5x^2 + 5) + 5 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(-1|x - 3| + 1) - 2)/(3(-1|x - 3| + 1) + 3))^2 + 4((1(-1|x - 3| + 1) - 2)/(3(-1|x - 3| + 1) + 3)) - 4 and g(x) = 2cos(2π(1|x + 2|) + 3) - 2 intersect in the interval [-10, 10].

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


[User]
How many solutions does the equation -2sin(1π((1((-1x - 2)/(-3x - 2)) - 1)/(1((-1x - 2)/(-3x - 2)))) + 1) = (1(-3x^2 - 1x - 2) - 2)/(3(-3x^2 - 1x - 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(3cos(1π((2x + 3)/(1x + 1)) + 2) + 1)^2 - 1 and g(x) = 3(3sin(3πx - 1) + 3)^2 + 3(3sin(3πx - 1) + 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) = -2|(-5(5x^2 - 3x - 3) - 1) - 1| + 1 and g(x) = (-2((-2x)/(1x + 1)) - 3)/(2((-2x)/(1x + 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) = 3(-1cos(3π(-1|x + 3| - 2) - 2) - 3) - 1 and g(x) = -2(-2sin(3πx + 1) + 2)^2 + 4(-2sin(3πx + 1) + 2) - 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) = 2cos(3π(-1|(-5x - 4) + 1| - 3) + 2) and g(x) = -3|((3x + 1)/(2x + 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 4(-3cos(1π(-2x - 1) - 2) + 1)^2 + 2(-3cos(1π(-2x - 1) - 2) + 1) = 4(-2e^(-2x) + 1)^2 + 3(-2e^(-2x) + 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) = (-1(-3((2x + 3)/(2x + 2))^2 - 1((2x + 3)/(2x + 2)) - 5) + 1)/(2(-3((2x + 3)/(2x + 2))^2 - 1((2x + 3)/(2x + 2)) - 5) + 2) and g(x) = -3sin(3π(-2x^2 - 2)) where -10 ≤ x ≤ 10.

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


[User]
How many solutions does the equation 2cos(1π(4(-5x^2 - 3x)^2 + 4(-5x^2 - 3x) + 4) + 1) - 2 = (-2(-2x^2 + 2x - 5) - 1)/(2(-2x^2 + 2x - 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) = -2|(-5(-1x^2 + 3x + 4)^2 - 1(-1x^2 + 3x + 4) + 2)| + 2 and g(x) = (-3(3|x + 2| - 1) - 3)/(2(3|x + 2| - 1) + 3) where -10 ≤ x ≤ 10.

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

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

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

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

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

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

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

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

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

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

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

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

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[User]
How many solutions does the equation 2sin(3π(3((-1x - 3)/(1x - 3))) - 1) + 1 = 2(3e^(1x) - 3)^2 - 2(3e^(1x) - 3) - 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) = -3|(1|(1x^2 + 2x) - 2| - 3)| + 3 and g(x) = (-1(-1|x + 2| + 2) - 1)/(3(-1|x + 2| + 2)) in the range -10 ≤ x ≤ 10?

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

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

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

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

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