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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


[User]
Find the number of times the graphs of f(x) = -3(-3(3sin(2π(-4(-1x - 4)) - 3) + 1)^2 + 1(3sin(2π(-4(-1x - 4)) - 3) + 1)) - 3 and g(x) = 1((2(-1(1x + 3) + 1) - 1)/(3(-1(1x + 3) + 1)))^2 - 5((2(-1(1x + 3) + 1) - 1)/(3(-1(1x + 3) + 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) = (-2((-3(-2cos(2π(1|(1x^2 + 4x + 1) + 1|) + 2)) - 1)/(-3(-2cos(2π(1|(1x^2 + 4x + 1) + 1|) + 2)) + 2)) + 1)/(-3((-3(-2cos(2π(1|(1x^2 + 4x + 1) + 1|) + 2)) - 1)/(-3(-2cos(2π(1|(1x^2 + 4x + 1) + 1|) + 2)) + 2))) and g(x) = 1|(-1(-1(1x^2 + 4x + 4) - 1)^2 - 3(-1(1x^2 + 4x + 4) - 1) + 5) + 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) = (-3(-3(-3cos(1π((1(-1x^2 + 1x - 1) + 1)/(-1(-1x^2 + 1x - 1) + 2))) - 1) - 1) + 2)/(-3(-3(-3cos(1π((1(-1x^2 + 1x - 1) + 1)/(-1(-1x^2 + 1x - 1) + 2))) - 1) - 1) - 3) and g(x) = (-1(2(-2(-1|x - 1| + 2))^2 + 3(-2(-1|x - 1| + 2)) - 4) - 3)/(-2(2(-2(-1|x - 1| + 2))^2 + 3(-2(-1|x - 1| + 2)) - 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) = 2(-1|(-2|(2|(-1sin(2πx - 3)) + 1| + 1) + 1| + 2) - 2| - 3)^2 - 2(-1|(-2|(2|(-1sin(2πx - 3)) + 1| + 1) + 1| + 2) - 2| - 3) - 5 and g(x) = 3e^(-1(-1|(5(-1|x - 2| + 3) - 3) + 3| + 3)) + 1 where -10 ≤ x ≤ 10.

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


[User]
Determine the number of intersection points between the functions f(x) = 3cos(2π(2((-2(-3(1|x - 3|) + 2) - 3)/(3(-3(1|x - 3|) + 2))) - 2) + 1) + 1 and g(x) = (-3(1e^(-1((1((2x + 2)/(-3x + 4)) - 3)/(-1((2x + 2)/(-3x + 4)) - 1))) - 2))/(-3(1e^(-1((1((2x + 2)/(-3x + 4)) - 3)/(-1((2x + 2)/(-3x + 4)) - 1))) - 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) = 3((-3(2(5(-1|x + 1| + 1) + 3) + 2) + 2)/(2(2(5(-1|x + 1| + 1) + 3) + 2) - 1)) + 5 and g(x) = -3cos(3π(5(-2((2x - 1)/(1x + 1))^2 - 2((2x - 1)/(1x + 1)) + 4) + 4)) + 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((-3(-2(3|x|) - 5) - 1)/(-2(-2(3|x|) - 5) + 3)) - 1)/(2((-3(-2(3|x|) - 5) - 1)/(-2(-2(3|x|) - 5) + 3)) - 1))^2 + 5((-2((-3(-2(3|x|) - 5) - 1)/(-2(-2(3|x|) - 5) + 3)) - 1)/(2((-3(-2(3|x|) - 5) - 1)/(-2(-2(3|x|) - 5) + 3)) - 1)) + 4 = -1(2(-1|((-2x + 2)/(2x + 2)) - 3| + 2)^2 + 1(-1|((-2x + 2)/(2x + 2)) - 3| + 2) + 1)^2 + 2(2(-1|((-2x + 2)/(2x + 2)) - 3| + 2)^2 + 1(-1|((-2x + 2)/(2x + 2)) - 3| + 2) + 1) + 3 have for x in the interval [-10, 10]?

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


[User]
Find the number of times the graphs of f(x) = (-3(-1(1|(-1(-1x^2 + 5x - 5)^2 - 2(-1x^2 + 5x - 5) + 3) + 3| - 3)^2 - 4(1|(-1(-1x^2 + 5x - 5)^2 - 2(-1x^2 + 5x - 5) + 3) + 3| - 3)) - 3)/(3(-1(1|(-1(-1x^2 + 5x - 5)^2 - 2(-1x^2 + 5x - 5) + 3) + 3| - 3)^2 - 4(1|(-1(-1x^2 + 5x - 5)^2 - 2(-1x^2 + 5x - 5) + 3) + 3| - 3)) - 1) and g(x) = (2(-2|(-2|(2cos(3πx - 1) + 3) + 1| - 1) + 1| - 3))/(1(-2|(-2|(2cos(3πx - 1) + 3) + 1| - 1) + 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) = (3((1(-3|(5(-3x^2 + 2)^2 + 4(-3x^2 + 2) + 3) - 2|) - 1)/(2(-3|(5(-3x^2 + 2)^2 + 4(-3x^2 + 2) + 3) - 2|) + 2)) - 2)/(2((1(-3|(5(-3x^2 + 2)^2 + 4(-3x^2 + 2) + 3) - 2|) - 1)/(2(-3|(5(-3x^2 + 2)^2 + 4(-3x^2 + 2) + 3) - 2|) + 2)) + 3) and g(x) = -2|(-1|(5((3x + 3)/(1x - 2))^2 + 1((3x + 3)/(1x - 2)) - 5) - 3| + 2) + 1| + 1 in the range -10 ≤ x ≤ 10?

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


[User]
Determine the number of intersection points between the functions f(x) = 2cos(1π((-3(-3(5((2x + 2)/(2x - 1))^2 + 3) + 3) - 1)/(3(-3(5((2x + 2)/(2x - 1))^2 + 3) + 3)))) + 3 and g(x) = -2cos(2π((2(-3((-2x + 1)/(1x))^2 - 4((-2x + 1)/(1x)) + 2) - 2)/(2(-3((-2x + 1)/(1x))^2 - 4((-2x + 1)/(1x)) + 2) + 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) = -3((3((1((1(-1e^(1x) + 2) + 2)/(-2(-1e^(1x) + 2) + 3)) + 2)/(3((1(-1e^(1x) + 2) + 2)/(-2(-1e^(1x) + 2) + 3)) - 2)) + 3)/(1((1((1(-1e^(1x) + 2) + 2)/(-2(-1e^(1x) + 2) + 3)) + 2)/(3((1(-1e^(1x) + 2) + 2)/(-2(-1e^(1x) + 2) + 3)) - 2)) - 3)) - 1 and g(x) = -1((1(-2|(2sin(2πx + 1) - 1) - 3| - 1) - 3)/(-3(-2|(2sin(2πx + 1) - 1) - 3| - 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) = 2|(2(-1cos(2π(1(1x - 3)^2 - 2(1x - 3) - 1)) + 1)^2 - 3(-1cos(2π(1(1x - 3)^2 - 2(1x - 3) - 1)) + 1) + 3) - 2| - 3 and g(x) = 2|(3((2(3cos(2πx - 3)) + 1)/(1(3cos(2πx - 3)) + 3))^2 - 2((2(3cos(2πx - 3)) + 1)/(1(3cos(2πx - 3)) + 3)) + 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 4(1(-2|(2cos(3π(-1x^2 + 4x + 2) + 3) - 1) - 2| + 2)^2 + 1(-2|(2cos(3π(-1x^2 + 4x + 2) + 3) - 1) - 2| + 2)) + 5 = 5(-1|(-2|(-3cos(1πx - 2) + 2) + 3| - 2) - 2| + 1)^2 + 4(-1|(-2|(-3cos(1πx - 2) + 2) + 3| - 2) - 2| + 1) - 4 have for x in the interval [-10, 10]?

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


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

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


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

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


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

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


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

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


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

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