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

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

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


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

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


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

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

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


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

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


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

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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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

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

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


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

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


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

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


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

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


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

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


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

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

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


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

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

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


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

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

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


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

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


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

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


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

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

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

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

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

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

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

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


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

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

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

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


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

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

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

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


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

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

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


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

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


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

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

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

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


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

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

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

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

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


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

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


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

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


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

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

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


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

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


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

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


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

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

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


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

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

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

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

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

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

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

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

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


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

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

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

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

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


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

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

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

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

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

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


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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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


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

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

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

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

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

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


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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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


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

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


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

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

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

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

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

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

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


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

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


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

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

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


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

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


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

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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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

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


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

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


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

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


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

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

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

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

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

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


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

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

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


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

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

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

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


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

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

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


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

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

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


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

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


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

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


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

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


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

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

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


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

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


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

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

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

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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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

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

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


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

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


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

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

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

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


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

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

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

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


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

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

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

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

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

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

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


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

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


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

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

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

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

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


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

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

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

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


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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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