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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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

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


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

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


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

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

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


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

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

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

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


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

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


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

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


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

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

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

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


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

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


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

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


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

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


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

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

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


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

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

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

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

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

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


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

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


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

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


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

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

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


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

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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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

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

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


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

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


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

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


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

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

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

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


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

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


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

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


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

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


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

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


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

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

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


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

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


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

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


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

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

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


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

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


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

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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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

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

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

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

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

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


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

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

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


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

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


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

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

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


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

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

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


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

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


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

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

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


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

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


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

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

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


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

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


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

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


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

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


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

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


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

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

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

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

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

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

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

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

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

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

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

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

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

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


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

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

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


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

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

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

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


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

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

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


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

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


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

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


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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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


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

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

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

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

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

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

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

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

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

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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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


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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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