messages listlengths 1 1 | ground_truth stringlengths 1 4 | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "How many solutions does the equation -3((1(-1|((1x - 1)/(-3x + 1)) - 2| + 2) - 1)/(-2(-1|((1x - 1)/(-3x + 1)) - 2| + 2) + 3)) - 3 = 1(2sin(2π(-1|x - 2| + 1) - 3) - 2)^2 - 4(2sin(2π(-1|x - 2| + 1) - 3) - 2) - 2 have for x in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{You... | 39 | MATH |
[
{
"content": "How many solutions does the equation 2(1|(5(-3sin(2πx + 2) + 2) + 2) + 1|)^2 + 5(1|(5(-3sin(2πx + 2) + 2) + 2) + 1|) + 2 = 1|((-3(-2e^(1x) + 2) + 3)/(-2(-2e^(1x) + 2) + 3)) + 1| + 1 have for x in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "use... | 79 | MATH |
[
{
"content": "How many points of intersection exist between the functions f(x) = 4(-1(-2(3|x - 2| - 3) - 3) + 1) and g(x) = -5(-2(2cos(3πx)))^2 + 2(-2(2cos(3πx))) + 3 in the range -10 ≤ x ≤ 10?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the number of intersection points between the functions f(x) = (1(-3|(1e^(-2(2|x + 3| - 1)) - 3) - 1| + 2) + 2)/(3(-3|(1e^(-2(2|x + 3| - 1)) - 3) - 1| + 2)) and g(x) = (-3(2(3|x + 1| - 1) + 1) + 1)/(-2(2(3|x + 1| - 1) + 1)) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\box... | 6 | MATH |
[
{
"content": "Find the number of times the graphs of f(x) = 4(2(-1((1x - 2)/(-2x - 2)) + 2) - 1) + 1 and g(x) = -4(-1sin(3π((-2x + 3)/(3x + 2)) - 3) + 1)^2 - 5 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 18 | MATH |
[
{
"content": "Find the number of times the graphs of f(x) = 2|(-1|(1|((-2x - 3)/(3x + 2)) - 1| - 1) + 1| + 3) - 1| and g(x) = -1cos(1π(2((-2x - 1)/(1x)) + 2)) + 2 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 18 | MATH |
[
{
"content": "Determine the number of intersection points between the functions f(x) = 3sin(3π(4(-1(-2x - 2))^2 + 2(-1(-2x - 2))) + 2) + 1 and g(x) = -5(-3e^(2((1x - 2)/(2x + 2))))^2 + 3(-3e^(2((1x - 2)/(2x + 2)))) + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role":... | 73 | MATH |
[
{
"content": "How many points of intersection exist between the functions f(x) = 5((1((3(2x^2 - 2x + 2))/(-2(2x^2 - 2x + 2) - 3)))/(-1((3(2x^2 - 2x + 2))/(-2(2x^2 - 2x + 2) - 3)) + 2)) + 3 and g(x) = 3(4(-3cos(3πx) + 2) + 2)^2 in the range -10 ≤ x ≤ 10?\n\nPresent the answer in LaTex format: \\boxed{Your answer... | 120 | MATH |
[
{
"content": "Determine the number of intersection points between the functions f(x) = (-2(-1((3(2|x - 1| - 3) - 3)/(2(2|x - 1| - 3) - 3))) + 1)/(2(-1((3(2|x - 1| - 3) - 3)/(2(2|x - 1| - 3) - 3))) + 1) and g(x) = 1(-5(-1cos(2πx - 3) - 1)^2 + 5(-1cos(2πx - 3) - 1) + 4) - 4 where -10 ≤ x ≤ 10.\n\nPresent the answ... | 38 | MATH |
[
{
"content": "How many solutions does the equation -4(-1((-2(-3x^2 + 2) - 3)/(-2(-3x^2 + 2) + 3)) + 1)^2 - 3(-1((-2(-3x^2 + 2) - 3)/(-2(-3x^2 + 2) + 3)) + 1) + 2 = 3|(3|(1x - 3) - 3| - 2) - 3| + 1 have for x in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "us... | 4 | MATH |
[
{
"content": "How many solutions does the equation (-2((2(-3|(-1x + 3) - 2| + 1) + 1)/(1(-3|(-1x + 3) - 2| + 1) + 3)))/(-2((2(-3|(-1x + 3) - 2| + 1) + 1)/(1(-3|(-1x + 3) - 2| + 1) + 3)) + 3) = -4(-3(-3sin(2πx - 3) - 1) + 1) - 1 have for x in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed... | 40 | MATH |
[
{
"content": "How many solutions does the equation -3(-2cos(3π(2|(-5x^2 + 5x - 3) - 1| - 2) + 3) - 2) + 1 = (2(-1|(-2|x + 2| - 2)|))/(1(-1|(-2|x + 2| - 2)|)) have for x in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 929 | MATH |
[
{
"content": "How many points of intersection exist between the functions f(x) = -2(3e^(-1(5(2|x|)^2 + 3(2|x|) - 2)) - 3)^2 - 4(3e^(-1(5(2|x|)^2 + 3(2|x|) - 2)) - 3) + 1 and g(x) = -2(1e^(-2(-4x^2 + 2x + 2)) - 1) - 1 in the range -10 ≤ x ≤ 10?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"r... | 6 | MATH |
[
{
"content": "How many solutions does the equation 1(1e^(-2(5(-4x^2 + 5x) - 4)) - 3)^2 + 1(1e^(-2(5(-4x^2 + 5x) - 4)) - 3) - 1 = -2sin(3π(-4(-2|x - 1| - 3) + 4) + 1) + 3 have for x in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 13 | MATH |
[
{
"content": "How many points of intersection exist between the functions f(x) = 3sin(1π(-2(-2|(5x^2 - 2x + 4) + 1|) - 1) + 3) - 1 and g(x) = 1(-1|(3sin(2πx - 3) + 1) + 2| + 2) in the range -10 ≤ x ≤ 10?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1112 | MATH |
[
{
"content": "Find the number of times the graphs of f(x) = 1cos(3π(1(2(5x - 1)^2 - 1(5x - 1) + 3) + 4) + 1) + 3 and g(x) = -2sin(3π(-3|(2x^2 - 2x + 3) + 1| - 2) + 3) + 3 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1222 | MATH |
[
{
"content": "How many solutions does the equation 5((3(-3sin(2π(1x - 5) + 1) + 2) + 2)/(-2(-3sin(2π(1x - 5) + 1) + 2) + 1)) - 1 = 3|(1|(-2|x - 2| - 3) - 1|) + 1| - 1 have for x in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
[
{
"content": "Find the number of times the graphs of f(x) = -2|(1|((-3(-1cos(1πx - 3) - 3) - 1)/(-2(-1cos(1πx - 3) - 3) - 3)) - 2| - 2) + 1| - 2 and g(x) = -3cos(2π(4((3x)/(-3x + 2)) - 2) + 2) - 1 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "use... | 73 | MATH |
[
{
"content": "How many points of intersection exist between the functions f(x) = -2e^(-1((-3(1(3|x - 1| + 3)^2 + 2(3|x - 1| + 3) - 4))/(1(1(3|x - 1| + 3)^2 + 2(3|x - 1| + 3) - 4) + 2))) - 1 and g(x) = -5(-1(2sin(2πx - 3) + 2) + 4)^2 + 2 in the range -10 ≤ x ≤ 10?\n\nPresent the answer in LaTex format: \\boxed{Y... | 40 | MATH |
[
{
"content": "How many solutions does the equation 2(-2|(-2|(1x + 2) + 3| + 2)| - 3)^2 - 1(-2|(-2|(1x + 2) + 3| + 2)| - 3) - 4 = 1(5(1e^(1x) - 1)^2 - 5(1e^(1x) - 1) + 3)^2 - 5(5(1e^(1x) - 1)^2 - 5(1e^(1x) - 1) + 3) - 2 have for x in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your ans... | 5 | MATH |
[
{
"content": "How many points of intersection exist between the functions f(x) = -3sin(3π(2|(1(-3|x| - 3)^2 - 4(-3|x| - 3) - 2) + 3| - 3) - 2) and g(x) = -3e^(1(5(5x + 3) + 5)) - 2 in the range -10 ≤ x ≤ 10?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 583 | MATH |
[
{
"content": "How many points of intersection exist between the functions f(x) = (-2(3((-2((-2x)/(3x + 1)) - 3)/(2((-2x)/(3x + 1))))) + 3)/(-1(3((-2((-2x)/(3x + 1)) - 3)/(2((-2x)/(3x + 1))))) + 3) and g(x) = -2(-5(3sin(2πx - 3) - 1) + 4)^2 + 2(-5(3sin(2πx - 3) - 1) + 4) - 5 in the range -10 ≤ x ≤ 10?\n\nPresent... | 5 | MATH |
[
{
"content": "How many solutions does the equation -3|(2(-3sin(2π((-3x + 1)/(-1x - 2)) + 1) - 2) - 1) + 1| + 2 = (1(5(-2|x + 1| - 3)) - 2)/(2(5(-2|x + 1| - 3)) + 3) have for x in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 83 | MATH |
[
{
"content": "Find the number of times the graphs of f(x) = (1(-4(-2sin(3π((-3x + 2)/(2x - 3)) - 2) - 3) - 5) - 2)/(-1(-4(-2sin(3π((-3x + 2)/(2x - 3)) - 2) - 3) - 5) + 3) and g(x) = -3(-1(1sin(2πx + 1) + 3) - 4) - 2 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}... | 5 | MATH |
[
{
"content": "How many points of intersection exist between the functions f(x) = (3(2sin(2π(1|(3x^2 + 2x - 2) - 3| - 1) - 3) + 3) + 3)/(2(2sin(2π(1|(3x^2 + 2x - 2) - 3| - 1) - 3) + 3) + 1) and g(x) = 2(1((-2x)/(-3x + 1))^2 + 3((-2x)/(-3x + 1)) - 2)^2 + 4(1((-2x)/(-3x + 1))^2 + 3((-2x)/(-3x + 1)) - 2) - 3 in the... | 15 | MATH |
[
{
"content": "Find the number of times the graphs of f(x) = -2(-1|(1(-2cos(2πx - 3) - 1)^2 - 1(-2cos(2πx - 3) - 1) - 4) - 3| + 3) - 2 and g(x) = 2cos(2π(-2|(1x^2 + 1x + 5) - 2| + 2) - 2) + 3 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}... | 167 | MATH |
[
{
"content": "Find the number of times the graphs of f(x) = -2sin(2π(-2|(-1|((2x - 3)/(-3x + 1)) + 1| + 2) + 3| + 1) - 2) + 2 and g(x) = -2(-2sin(2π(-2x + 2) - 3) + 3)^2 + 2(-2sin(2π(-2x + 2) - 3) + 3) + 4 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"ro... | 89 | MATH |
[
{
"content": "How many solutions does the equation -3cos(2π((-2(-1(-5x - 5)^2 + 3) - 3)/(-1(-1(-5x - 5)^2 + 3) + 3)) - 2) + 3 = (-1(1(-3x - 1) + 3))/(-2(1(-3x - 1) + 3) - 2) have for x in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 36 | MATH |
[
{
"content": "How many solutions does the equation 3|((-1(2|(3|x + 2| + 1) - 1| - 3) + 2)/(-2(2|(3|x + 2| + 1) - 1| - 3)))| + 1 = -2sin(1π(-5(-2|x - 2| + 2)^2 + 4(-2|x - 2| + 2)) - 1) + 2 have for x in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1427 | MATH |
[
{
"content": "How many points of intersection exist between the functions f(x) = 1e^(-1(-2|((-1(3x^2 - 1x - 1))/(-1(3x^2 - 1x - 1) + 2)) - 3| + 2)) - 3 and g(x) = 2|((-1(2|x + 1| - 3) + 2)/(2(2|x + 1| - 3) - 1)) - 3| - 1 in the range -10 ≤ x ≤ 10?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 6 | MATH |
[
{
"content": "How many solutions does the equation -3sin(1π(-2|(4(5x^2 + 2x)^2 + 4(5x^2 + 2x) + 5) + 3| - 3) - 1) + 3 = -2cos(3π(-3|(2|x - 2| + 1)| + 2) - 3) + 3 have for x in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 648 | MATH |
[
{
"content": "How many solutions does the equation -3|(-4((-1(-1x + 1) - 1)/(2(-1x + 1) - 3))^2 - 2((-1(-1x + 1) - 1)/(2(-1x + 1) - 3)) + 3) - 2| = (1((2((-3x + 1)/(-3x - 2)) - 3)/(3((-3x + 1)/(-3x - 2)) + 3)) - 2)/(2((2((-3x + 1)/(-3x - 2)) - 3)/(3((-3x + 1)/(-3x - 2)) + 3)) + 2) have for x in the interval [-1... | 5 | MATH |
[
{
"content": "How many solutions does the equation (-1(-3|(2cos(3π(3|x - 1|) - 1) + 1) - 2| + 3) + 3)/(-1(-3|(2cos(3π(3|x - 1|) - 1) + 1) - 2| + 3) + 2) = 3|(-1(4x + 5)^2 + 1(4x + 5)) - 3| + 3 have for x in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 8 | MATH |
[
{
"content": "Find the number of times the graphs of f(x) = 1|(3(-2cos(2π((1x - 3)/(3x + 1)) - 2) + 3) + 4)| and g(x) = (-3((2(1x - 5) + 1)/(-3(1x - 5) + 1)) + 1)/(-2((2(1x - 5) + 1)/(-3(1x - 5) + 1)) - 1) intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"ro... | 9 | MATH |
[
{
"content": "How many solutions does the equation (-1(-1(2(1x^2 + 5x - 2) - 1) + 3) - 1)/(-1(-1(2(1x^2 + 5x - 2) - 1) + 3) + 2) = 1(-2(1x^2 + 5x + 1) - 2)^2 - 3(-2(1x^2 + 5x + 1) - 2) - 5 have for x in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
... | 4 | MATH |
[
{
"content": "Determine the number of intersection points between the functions f(x) = 1|(1e^(-1(2|((2x)/(-2x))| - 2))) - 2| + 1 and g(x) = 1(2|(3|x - 3| - 2) - 2|)^2 - 5(2|(3|x - 3| - 2) - 2|) - 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the number of times the graphs of f(x) = -5(-5(3(1cos(1πx) + 1)^2 - 3(1cos(1πx) + 1) - 2)^2 + 2(3(1cos(1πx) + 1)^2 - 3(1cos(1πx) + 1) - 2) + 5)^2 - 5(-5(3(1cos(1πx) + 1)^2 - 3(1cos(1πx) + 1) - 2)^2 + 2(3(1cos(1πx) + 1)^2 - 3(1cos(1πx) + 1) - 2) + 5) + 3 and g(x) = 3sin(2π(-5(3|x - 2| + 1)^2 -... | 60 | MATH |
[
{
"content": "Find the number of times the graphs of f(x) = 3(3e^(-1((2(-1x^2 - 2x + 2) + 1)/(2(-1x^2 - 2x + 2)))))^2 - 1(3e^(-1((2(-1x^2 - 2x + 2) + 1)/(2(-1x^2 - 2x + 2))))) + 4 and g(x) = 3(1(-2|x + 1| - 3)^2 + 4(-2|x + 1| - 3) + 5)^2 - 4(1(-2|x + 1| - 3)^2 + 4(-2|x + 1| - 3) + 5) - 1 intersect in the interv... | 4 | MATH |
[
{
"content": "How many points of intersection exist between the functions f(x) = 3(-1(-2(1cos(2πx + 1) - 2)^2 + 1(1cos(2πx + 1) - 2) + 2) - 5) + 5 and g(x) = 5(-1sin(2π((-1x + 1)/(1x + 3)) + 2)) + 1 in the range -10 ≤ x ≤ 10?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 51 | MATH |
[
{
"content": "Determine the number of intersection points between the functions f(x) = (-2((-2(-1cos(2π((1x - 1)/(3x - 2)) - 1) - 2) - 3)/(-1(-1cos(2π((1x - 1)/(3x - 2)) - 1) - 2) + 2)) + 1)/(-1((-2(-1cos(2π((1x - 1)/(3x - 2)) - 1) - 2) - 3)/(-1(-1cos(2π((1x - 1)/(3x - 2)) - 1) - 2) + 2)) - 3) and g(x) = (-3(-2... | 4 | MATH |
[
{
"content": "How many points of intersection exist between the functions f(x) = -4(3(4(-3|x + 2| + 3) - 4)^2 + 5(4(-3|x + 2| + 3) - 4) - 1)^2 + 3(3(4(-3|x + 2| + 3) - 4)^2 + 5(4(-3|x + 2| + 3) - 4) - 1) - 5 and g(x) = -5((-2(3|x + 1| - 3) - 3)/(2(3|x + 1| - 3) + 3))^2 + 2((-2(3|x + 1| - 3) - 3)/(2(3|x + 1| - 3... | 8 | MATH |
[
{
"content": "Find the number of times the graphs of f(x) = -2sin(2π(-3(-2|(-1|x| - 2)| - 3)^2 - 1(-2|(-1|x| - 2)| - 3) - 4) - 2) + 1 and g(x) = (-2((1(-2|x - 2| - 1) + 3)/(-3(-2|x - 2| - 1) + 1)))/(1((1(-2|x - 2| - 1) + 3)/(-3(-2|x - 2| - 1) + 1)) + 3) intersect in the interval [-10, 10].\n\nPresent the answer... | 1390 | MATH |
[
{
"content": "Determine the number of intersection points between the functions f(x) = 1(1((-2(-1|x - 2| + 2) - 3)/(2(-1|x - 2| + 2) - 1)))^2 + 3(1((-2(-1|x - 2| + 2) - 3)/(2(-1|x - 2| + 2) - 1))) - 4 and g(x) = 1|((-1(-4x - 1) + 3)/(2(-4x - 1) - 3))| + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex forma... | 4 | MATH |
[
{
"content": "Determine the number of intersection points between the functions f(x) = (-1(-3(3|((1x - 3)/(-1x + 2)) + 2| - 1)^2 + 3(3|((1x - 3)/(-1x + 2)) + 2| - 1) + 5))/(-1(-3(3|((1x - 3)/(-1x + 2)) + 2| - 1)^2 + 3(3|((1x - 3)/(-1x + 2)) + 2| - 1) + 5) + 2) and g(x) = -4(-2cos(1π(2|x| + 1) + 2) - 1) + 5 wher... | 14 | MATH |
[
{
"content": "Determine the number of intersection points between the functions f(x) = 2(-3(-2cos(3π((-2x + 2)/(2x)) - 3) - 1) - 4) + 5 and g(x) = -2(4(-1x^2 + 2x + 4)^2 - 1(-1x^2 + 2x + 4) - 1)^2 - 2(4(-1x^2 + 2x + 4)^2 - 1(-1x^2 + 2x + 4) - 1) - 4 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\b... | 4 | MATH |
[
{
"content": "How many points of intersection exist between the functions f(x) = 1(3(-2|(1x^2 + 5x - 1) + 1| - 1) + 1)^2 + 2(3(-2|(1x^2 + 5x - 1) + 1| - 1) + 1) - 3 and g(x) = 4(-2e^(1(2x - 3))) - 1 in the range -10 ≤ x ≤ 10?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the number of times the graphs of f(x) = 1(-4(2(2e^(-1x) - 3)^2 - 2(2e^(-1x) - 3) - 3)^2 + 1(2(2e^(-1x) - 3)^2 - 2(2e^(-1x) - 3) - 3) + 1) + 4 and g(x) = -4((2(-3sin(3πx + 1) + 2))/(3(-3sin(3πx + 1) + 2) - 2))^2 + 2((2(-3sin(3πx + 1) + 2))/(3(-3sin(3πx + 1) + 2) - 2)) - 4 intersect in the int... | 24 | MATH |
[
{
"content": "Find the number of times the graphs of f(x) = (-1(-2(-3(-2|x|)^2 - 1(-2|x|) + 5)^2 - 3(-3(-2|x|)^2 - 1(-2|x|) + 5) + 1))/(-2(-2(-3(-2|x|)^2 - 1(-2|x|) + 5)^2 - 3(-3(-2|x|)^2 - 1(-2|x|) + 5) + 1) - 3) and g(x) = (2((-1(-1x^2 + 2x - 5))/(1(-1x^2 + 2x - 5) + 1)) + 2)/(-1((-1(-1x^2 + 2x - 5))/(1(-1x^2... | 4 | MATH |
[
{
"content": "How many points of intersection exist between the functions f(x) = -2|((3((3((2x)/(2x - 3)))/(3((2x)/(2x - 3)) - 2)))/(3((3((2x)/(2x - 3)))/(3((2x)/(2x - 3)) - 2)) - 1)) - 3| + 3 and g(x) = -5((-1((-1x - 2)/(3x + 3)) - 2)/(1((-1x - 2)/(3x + 3)) + 1))^2 + 2((-1((-1x - 2)/(3x + 3)) - 2)/(1((-1x - 2)... | 4 | MATH |
[
{
"content": "Determine the number of intersection points between the functions f(x) = -2|((2(4(2sin(3πx - 2) - 3)^2 + 4(2sin(3πx - 2) - 3) - 1) - 3)/(1(4(2sin(3πx - 2) - 3)^2 + 4(2sin(3πx - 2) - 3) - 1) + 1)) - 1| and g(x) = -2(1|(-4x^2 - 3x - 3) - 3| + 1) - 5 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex... | 60 | MATH |
[
{
"content": "Find the number of times the graphs of f(x) = (-1((2((1(-1x - 2) + 1)/(2(-1x - 2) + 1)))/(-2((1(-1x - 2) + 1)/(2(-1x - 2) + 1)))) + 1)/(-2((2((1(-1x - 2) + 1)/(2(-1x - 2) + 1)))/(-2((1(-1x - 2) + 1)/(2(-1x - 2) + 1)))) + 3) and g(x) = 3sin(1π(1((-3x - 1)/(-1x))^2 - 5((-3x - 1)/(-1x)) - 4) + 3) + 3... | 55 | MATH |
[
{
"content": "How many points of intersection exist between the functions f(x) = (-1(-4((3((2x + 2)/(-2x + 3)) + 3)/(-2((2x + 2)/(-2x + 3)) + 3))^2 + 4))/(1(-4((3((2x + 2)/(-2x + 3)) + 3)/(-2((2x + 2)/(-2x + 3)) + 3))^2 + 4) - 3) and g(x) = 4(2sin(1π(-1x^2 + 3x - 4)) + 3) - 5 in the range -10 ≤ x ≤ 10?\n\nPrese... | 18 | MATH |
[
{
"content": "Determine the number of intersection points between the functions f(x) = (-1((2(5(-1x + 4)^2 + 2(-1x + 4) + 2) + 2)/(1(5(-1x + 4)^2 + 2(-1x + 4) + 2) + 2)) + 2)/(-1((2(5(-1x + 4)^2 + 2(-1x + 4) + 2) + 2)/(1(5(-1x + 4)^2 + 2(-1x + 4) + 2) + 2)) - 1) and g(x) = -3sin(2π(3((-2x - 3)/(-1x - 3)) + 1) -... | 152 | MATH |
[
{
"content": "How many points of intersection exist between the functions f(x) = -3(-2|(-1|(-3sin(3πx - 1) + 1) - 3| + 2)| + 1) - 2 and g(x) = 1|(2|(-1x - 2) + 1| - 1) - 3| - 2 in the range -10 ≤ x ≤ 10?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 117 | MATH |
[
{
"content": "Determine the number of intersection points between the functions f(x) = (-1(-1|(1sin(3π(3x^2 + 5x) + 1) - 1) - 3| + 3) - 2)/(3(-1|(1sin(3π(3x^2 + 5x) + 1) - 1) - 3| + 3) + 3) and g(x) = 2(3|(-2x^2 - 3x + 1) - 3| + 2) + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answ... | 7 | MATH |
[
{
"content": "How many points of intersection exist between the functions f(x) = -4(3sin(1π((-3(-3|x + 3| + 3))/(1(-3|x + 3| + 3) + 2)) + 3) - 1)^2 - 2(3sin(1π((-3(-3|x + 3| + 3))/(1(-3|x + 3| + 3) + 2)) + 3) - 1) + 1 and g(x) = -2sin(1π(2(-4x^2 - 2x + 5) - 5) + 3) + 1 in the range -10 ≤ x ≤ 10?\n\nPresent the ... | 96 | MATH |
[
{
"content": "Find the number of times the graphs of f(x) = -2|(-5(-4(1x^2 + 4x + 1)^2 - 2(1x^2 + 4x + 1) + 1)^2 + 2(-4(1x^2 + 4x + 1)^2 - 2(1x^2 + 4x + 1) + 1) + 2)| - 2 and g(x) = -3|(4(-1e^(-2x) + 2) + 3)| + 2 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 7 | MATH |
[
{
"content": "Determine the number of intersection points between the functions f(x) = 3|(2|((-1((-2x + 1)/(-3x + 1)) + 3)/(1((-2x + 1)/(-3x + 1)) - 3)) + 3| - 3) - 1| - 1 and g(x) = -1cos(3π((-3(2x) - 3)/(2(2x) - 1)) - 3) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 66 | MATH |
[
{
"content": "How many points of intersection exist between the functions f(x) = 5(-1(1((1x - 1)/(3x + 2))^2 + 3((1x - 1)/(3x + 2)) + 5)^2 + 1(1((1x - 1)/(3x + 2))^2 + 3((1x - 1)/(3x + 2)) + 5) - 1) - 3 and g(x) = -4(-2sin(1π(5x^2 + 4x - 5) - 2) - 3)^2 + 1(-2sin(1π(5x^2 + 4x - 5) - 2) - 3) in the range -10 ≤ x ... | 8 | MATH |
[
{
"content": "Find the number of times the graphs of f(x) = -2cos(2π(-4(2(2x^2 - 5)) + 4) + 3) and g(x) = 5(-4((3x - 3)/(-1x)) + 1) - 3 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the number of intersection points between the functions f(x) = (3((3(5(-1|x| + 1) + 3) + 3)/(2(5(-1|x| + 1) + 3))) - 2)/(-3((3(5(-1|x| + 1) + 3) + 3)/(2(5(-1|x| + 1) + 3))) - 2) and g(x) = -2(1(-3cos(1πx + 3) - 2)^2 + 5(-3cos(1πx + 3) - 2))^2 - 1(1(-3cos(1πx + 3) - 2)^2 + 5(-3cos(1πx + 3... | 60 | MATH |
[
{
"content": "Determine the number of intersection points between the functions f(x) = -1|(2(5(-3x^2 + 2x - 4) + 4) - 1) + 2| - 3 and g(x) = 4(-3|((-1x - 3)/(1x - 3)) + 2| + 2) - 5 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the number of intersection points between the functions f(x) = -2|(-1(2(1x^2 - 1x - 3)^2 - 3(1x^2 - 1x - 3) + 4) - 2) + 3| + 3 and g(x) = 1(1e^(-2((-1x - 1)/(-3x + 2))) - 1)^2 + 5(1e^(-2((-1x - 1)/(-3x + 2))) - 1) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{You... | 4 | MATH |
[
{
"content": "How many points of intersection exist between the functions f(x) = -2|(-3(-3sin(2π(1|x + 3|) - 3) - 2)) + 1| - 1 and g(x) = -1|(2e^(-2(-2x - 1))) + 2| + 1 in the range -10 ≤ x ≤ 10?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 11 | MATH |
[
{
"content": "Determine the number of intersection points between the functions f(x) = -3|(2(-4(1x^2 + 5x - 5)^2 + 1(1x^2 + 5x - 5) - 2) + 4) + 1| + 3 and g(x) = -2|(-2|(3x^2 - 4x + 2) - 1| - 2) - 3| + 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the number of times the graphs of f(x) = 5(1(3|(-1|x + 2| + 1) - 1|)^2 + 3(3|(-1|x + 2| + 1) - 1|) - 4)^2 + 5(1(3|(-1|x + 2| + 1) - 1|)^2 + 3(3|(-1|x + 2| + 1) - 1|) - 4) + 1 and g(x) = (-2(-2cos(1π(4x - 4) + 2) - 1) + 3)/(-2(-2cos(1π(4x - 4) + 2) - 1)) intersect in the interval [-10, 10].\n\... | 4 | MATH |
[
{
"content": "How many solutions does the equation (1(1cos(3π((-3(5x - 5) + 1)/(3(5x - 5) + 2)) - 1) - 2) - 2)/(-3(1cos(3π((-3(5x - 5) + 1)/(3(5x - 5) + 2)) - 1) - 2) - 3) = (-2(-4(2x + 3)^2 + 1(2x + 3)) + 1)/(1(-4(2x + 3)^2 + 1(2x + 3)) - 3) have for x in the interval [-10, 10]?\n\nPresent the answer in LaTex ... | 28 | MATH |
[
{
"content": "How many points of intersection exist between the functions f(x) = 3e^(-1(3(3|(-1|x + 1|) - 2| - 2) + 3)) and g(x) = 3cos(2π(3((2x)/(-3x + 4))^2 + 2((2x)/(-3x + 4)) - 2) + 3) - 2 in the range -10 ≤ x ≤ 10?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 103 | MATH |
[
{
"content": "How many points of intersection exist between the functions f(x) = -4((-2(-1e^(1((-1x + 1)/(1x + 1))) - 2) + 3)/(2(-1e^(1((-1x + 1)/(1x + 1))) - 2) + 2)) + 2 and g(x) = 5(-2(-2sin(3πx) + 3)^2 + 4(-2sin(3πx) + 3) + 5) in the range -10 ≤ x ≤ 10?\n\nPresent the answer in LaTex format: \\boxed{Your an... | 60 | MATH |
[
{
"content": "Determine the number of intersection points between the functions f(x) = 2cos(1π(3(1((3x)/(-1x - 3)) + 4) - 1)) and g(x) = -1e^(-1(1(2|x - 3| + 3)^2 - 4(2|x - 3| + 3) + 3)) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 177 | MATH |
[
{
"content": "Find the number of times the graphs of f(x) = -4(-3cos(1π(1|(-2|x - 1| + 2) + 1| + 3) + 1)) + 4 and g(x) = (3(-2((3x + 2)/(2x + 1)) + 4) - 2)/(2(-2((3x + 2)/(2x + 1)) + 4) - 3) intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}... | 39 | MATH |
[
{
"content": "Determine the number of intersection points between the functions f(x) = -1|(-2|(3|((-2x - 1)/(-2x - 2)) - 1| + 1) - 3| + 2) - 1| + 2 and g(x) = (2(2|(1x^2 - 5x + 3) - 3| + 3) + 3)/(2(2|(1x^2 - 5x + 3) - 3| + 3) - 3) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",... | 6 | MATH |
[
{
"content": "How many solutions does the equation 2(-1e^(1((-2((-1x - 2)/(-3x + 2)) - 3)/(3((-1x - 2)/(-3x + 2)) - 2))) + 3) + 4 = (-2(3sin(3π(-1|x|)) - 2) - 3)/(-1(3sin(3π(-1|x|)) - 2)) have for x in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 37 | MATH |
[
{
"content": "Determine the number of intersection points between the functions f(x) = (2(-3|(-4(5x^2 + 5x)^2 - 5(5x^2 + 5x) - 1) + 2|))/(2(-3|(-4(5x^2 + 5x)^2 - 5(5x^2 + 5x) - 1) + 2|) + 1) and g(x) = (2(-1((2x - 2)/(2x - 1)) + 4) - 2)/(-2(-1((2x - 2)/(2x - 1)) + 4) + 1) where -10 ≤ x ≤ 10.\n\nPresent the answ... | 5 | MATH |
[
{
"content": "How many solutions does the equation 3(3cos(1π(-1(4x - 4) + 1) - 2)) - 3 = -5(-4(1sin(3πx + 1) + 2) + 5) + 3 have for x in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
[
{
"content": "Determine the number of intersection points between the functions f(x) = -2(2|((-3(2|x| - 1) - 3)/(-2(2|x| - 1) + 1)) - 2| + 1) + 4 and g(x) = 3|(-1(3cos(3πx) + 2)^2 + 5(3cos(3πx) + 2) + 1) + 2| - 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user... | 104 | MATH |
[
{
"content": "How many solutions does the equation (3(1(3((-2x)/(2x + 2))^2 + 1((-2x)/(2x + 2)) - 4)^2 - 2(3((-2x)/(2x + 2))^2 + 1((-2x)/(2x + 2)) - 4) - 2) + 1)/(-1(1(3((-2x)/(2x + 2))^2 + 1((-2x)/(2x + 2)) - 4)^2 - 2(3((-2x)/(2x + 2))^2 + 1((-2x)/(2x + 2)) - 4) - 2) + 3) = 3sin(3π(-3(-3x + 1)^2 - 1(-3x + 1) +... | 334 | MATH |
[
{
"content": "Determine the number of intersection points between the functions f(x) = -1sin(1π(3|(-4(-2x - 2)^2 - 3) + 1| - 3) - 1) + 2 and g(x) = 2|(3(-3x^2 + 2x + 1)^2 + 1(-3x^2 + 2x + 1) - 4) - 3| - 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 21 | MATH |
[
{
"content": "How many points of intersection exist between the functions f(x) = (-1(3cos(1π(2(5x - 5)^2 + 3(5x - 5) - 4) + 3) + 1) + 2)/(1(3cos(1π(2(5x - 5)^2 + 3(5x - 5) - 4) + 3) + 1) + 3) and g(x) = -4(-1(3sin(1πx) + 2) + 4)^2 + 3(-1(3sin(1πx) + 2) + 4) in the range -10 ≤ x ≤ 10?\n\nPresent the answer in La... | 186 | MATH |
[
{
"content": "Determine the number of intersection points between the functions f(x) = 3sin(1π(-1((-2(1x - 1) + 3)/(1(1x - 1) + 3)) - 1) + 1) - 3 and g(x) = (1(-3(-5x + 4)^2 - 2(-5x + 4) - 4) - 1)/(-3(-3(-5x + 4)^2 - 2(-5x + 4) - 4)) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer... | 67 | MATH |
[
{
"content": "Determine the number of intersection points between the functions f(x) = 4(5(-2sin(2π(4x^2 - 5x - 5) + 2) + 2)^2 - 2(-2sin(2π(4x^2 - 5x - 5) + 2) + 2) - 3) - 3 and g(x) = 3(1(-1|x - 2| - 1)^2 + 1(-1|x - 2| - 1) - 3) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer... | 972 | MATH |
[
{
"content": "Determine the number of intersection points between the functions f(x) = -3e^(-1(-5((2(-1|x + 3| + 3))/(1(-1|x + 3| + 3) - 2))^2 + 3((2(-1|x + 3| + 3))/(1(-1|x + 3| + 3) - 2)) + 1)) + 1 and g(x) = -1(-1|(-2sin(1πx - 2) + 3)| + 3) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\box... | 4 | MATH |
[
{
"content": "Determine the number of intersection points between the functions f(x) = 2(1cos(1π((-3(-1x - 2) - 1)/(1(-1x - 2) + 3)) - 3) + 3)^2 - 5(1cos(1π((-3(-1x - 2) - 1)/(1(-1x - 2) + 3)) - 3) + 3) - 5 and g(x) = 1(-1(-1sin(2πx - 1)) + 4)^2 - 1(-1(-1sin(2πx - 1)) + 4) - 4 where -10 ≤ x ≤ 10.\n\nPresent the... | 39 | MATH |
[
{
"content": "How many points of intersection exist between the functions f(x) = -2((1(-2|(2|x + 3| - 3) - 3| - 1) - 3)/(-1(-2|(2|x + 3| - 3) - 3| - 1) - 1))^2 - 5((1(-2|(2|x + 3| - 3) - 3| - 1) - 3)/(-1(-2|(2|x + 3| - 3) - 3| - 1) - 1)) + 1 and g(x) = 1((-2(-1|x + 3| - 3))/(-3(-1|x + 3| - 3) + 2))^2 + 3((-2(-1... | 4 | MATH |
[
{
"content": "Find the number of times the graphs of f(x) = 1|(-1cos(3π((-2(-3x^2 + 5x + 5) + 2)/(-2(-3x^2 + 5x + 5) - 3)) + 2) - 3) + 1| + 2 and g(x) = 1(-3e^(2(-1|x - 2| + 3)) + 1) + 5 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "How many points of intersection exist between the functions f(x) = -4((-2(-2sin(3π(-1x + 3) + 2) + 2) + 1)/(3(-2sin(3π(-1x + 3) + 2) + 2) - 1))^2 + 1((-2(-2sin(3π(-1x + 3) + 2) + 2) + 1)/(3(-2sin(3π(-1x + 3) + 2) + 2) - 1)) + 5 and g(x) = (-2(-1e^(-1(3x - 1))))/(-1(-1e^(-1(3x - 1))) - 2) in the ra... | 74 | MATH |
[
{
"content": "How many points of intersection exist between the functions f(x) = 1cos(2π(-5(-2(1x + 1) - 1)^2 - 1(-2(1x + 1) - 1) - 4) + 3) + 2 and g(x) = (2(-3(1x^2 - 3) - 1) + 1)/(3(-3(1x^2 - 3) - 1) - 1) in the range -10 ≤ x ≤ 10?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "use... | 9 | MATH |
[
{
"content": "Find the number of times the graphs of f(x) = -2|(3((2(3x^2 - 5x + 2) - 1)/(1(3x^2 - 5x + 2)))^2 - 1((2(3x^2 - 5x + 2) - 1)/(1(3x^2 - 5x + 2))) - 4) - 1| + 2 and g(x) = -2sin(2π(3(1x^2 - 5x + 2) - 2) + 1) - 1 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your ... | 23 | MATH |
[
{
"content": "Find the number of times the graphs of f(x) = 3|(4(1cos(2π(-1|x| + 2) - 2) + 3) - 5) - 1| - 3 and g(x) = 3|(2|((1x - 3)/(1x - 3)) + 2| - 3) - 3| + 3 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20 | MATH |
[
{
"content": "Determine the number of intersection points between the functions f(x) = 4(-5(-5(-1sin(2πx - 2))^2 - 5(-1sin(2πx - 2)) + 3))^2 + 3(-5(-5(-1sin(2πx - 2))^2 - 5(-1sin(2πx - 2)) + 3)) - 5 and g(x) = (-2(-3e^(-2(-3|x - 2| - 2)) - 1))/(1(-3e^(-2(-3|x - 2| - 2)) - 1) - 2) where -10 ≤ x ≤ 10.\n\nPresent ... | 60 | MATH |
[
{
"content": "How many points of intersection exist between the functions f(x) = 3|(3|((-3(-5x - 2))/(-3(-5x - 2) - 3)) - 1| - 3)| + 1 and g(x) = -1sin(1π(-1|(1x + 5) + 3| - 1) - 1) + 3 in the range -10 ≤ x ≤ 10?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "How many points of intersection exist between the functions f(x) = (1(-1|(-2(-5x^2 + 4x - 3)^2 - 2(-5x^2 + 4x - 3)) - 3| + 1) - 1)/(-1(-1|(-2(-5x^2 + 4x - 3)^2 - 2(-5x^2 + 4x - 3)) - 3| + 1) + 2) and g(x) = -4(3cos(3π(5x + 3) - 3)) + 5 in the range -10 ≤ x ≤ 10?\n\nPresent the answer in LaTex form... | 300 | MATH |
[
{
"content": "Determine the number of intersection points between the functions f(x) = 3((1(-3cos(2π(-4x^2 + 3x + 4) + 2) - 2) - 1)/(-1(-3cos(2π(-4x^2 + 3x + 4) + 2) - 2) + 3)) - 1 and g(x) = (-2(-3((-3x + 3)/(-3x + 1)) + 1) + 1)/(3(-3((-3x + 3)/(-3x + 1)) + 1) + 1) where -10 ≤ x ≤ 10.\n\nPresent the answer in ... | 173 | MATH |
[
{
"content": "Determine the number of intersection points between the functions f(x) = (-1(-3(1|(-1x + 2) - 1| - 1) + 4) + 2)/(2(-3(1|(-1x + 2) - 1| - 1) + 4) + 1) and g(x) = -1|(-4(-3|x + 1| + 3) - 1) + 3| - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 4 | MATH |
[
{
"content": "How many points of intersection exist between the functions f(x) = -4(3(2sin(3π(1|x - 2| + 1) - 3) - 3) - 5) + 1 and g(x) = 3|(1(-1x - 2) - 5) + 1| + 1 in the range -10 ≤ x ≤ 10?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 16 | MATH |
[
{
"content": "Find the number of times the graphs of f(x) = (-2((3(1(1sin(2πx) + 1) + 4) + 3)/(-3(1(1sin(2πx) + 1) + 4) + 2)))/(1((3(1(1sin(2πx) + 1) + 4) + 3)/(-3(1(1sin(2πx) + 1) + 4) + 2)) - 3) and g(x) = 4(2sin(3π((-1x - 3)/(3x + 1)) - 2) - 1)^2 - 1(2sin(3π((-1x - 3)/(3x + 1)) - 2) - 1) - 4 intersect in the... | 58 | MATH |
[
{
"content": "How many solutions does the equation -1(-3((-1(-3e^(1x) + 1) - 2)/(-2(-3e^(1x) + 1) + 3))^2 - 2((-1(-3e^(1x) + 1) - 2)/(-2(-3e^(1x) + 1) + 3)))^2 + 5(-3((-1(-3e^(1x) + 1) - 2)/(-2(-3e^(1x) + 1) + 3))^2 - 2((-1(-3e^(1x) + 1) - 2)/(-2(-3e^(1x) + 1) + 3))) + 2 = (-2(-3sin(2π(1x - 2) - 3) - 3) + 1)/(-... | 25 | MATH |
[
{
"content": "How many solutions does the equation (3(1(-5(1e^(2x) - 3)) - 2) + 3)/(3(1(-5(1e^(2x) - 3)) - 2) - 2) = (-3(-3cos(3π(1x^2 + 5x + 1) + 2) - 1) - 1)/(-1(-3cos(3π(1x^2 + 5x + 1) + 2) - 1)) have for x in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "... | 292 | MATH |
[
{
"content": "Find the number of times the graphs of f(x) = (-2(-2sin(2π(-5(-5x - 5)^2 - 4(-5x - 5) - 2) + 1) + 1) + 1)/(2(-2sin(2π(-5(-5x - 5)^2 - 4(-5x - 5) - 2) + 1) + 1) + 2) and g(x) = 2|(3cos(2π((-1x - 3)/(2x + 1)) + 1) - 3) + 2| - 1 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex form... | 814 | MATH |
[
{
"content": "Determine the number of intersection points between the functions f(x) = -2e^(1(1(-1|((-2x)/(-3x - 2)) + 3| + 2)^2 + 2(-1|((-2x)/(-3x - 2)) + 3| + 2) - 3)) + 2 and g(x) = 1cos(2π(5(-1x^2 + 4) + 3) + 2) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "u... | 6 | MATH |
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