F (x) = (m-1) x ^ 2 + (m-2) x + (m ^ 2-7m + 12), X ∈ [3-A, 5] is even function, find the value of a, M

F (x) = (m-1) x ^ 2 + (m-2) x + (m ^ 2-7m + 12), X ∈ [3-A, 5] is even function, find the value of a, M

The domain is symmetric, so a = 8
Even function, m-2 = 0, so m = 2

The increasing function y = f (x) is defined on (- 1,1) and is an odd function. If f (1-m) + F (1-m ^ 2) > 0, the value range of real number m is obtained

f(1-m)+f(1-m^2)>0
f(1-m)>-f(1-m^2)
F (x) is an odd function, so
f(1-m)>f(m^2-1)
Y = f (x) is defined on (- 1,1), so
-1

The increasing function y = f (x) is defined on (- 1,1) and is odd. If f (1-m) + F (1-mm) > 0, the value range of real number m is obtained

Since y = f (x) is defined on (- 1,1)
So - 1

Let f (x) be a decreasing function defined on (- 2,2) and satisfy the following conditions: F (- x) = - f (x), and f (m-1) + F (2m-1) > 0, then the value range of real number m is obtained

The inequality f (m-1) + F (2m-1) > 0, that is, f (m-1) > F (2m-1), ∵ f (- x) = - f (x), we can get - f (2m-1) = f (- 2m + 1) ∵ the original inequality is transformed into f (m-1) > F (- 2m + 1) and ∵ f (x) is a decreasing function defined on (- 2,2), ∵ - 2 ＜ M-1 ＜ - 2m + 1 ＜ 2

If the function f (x) is a decreasing function on R, and f (- x) = - f (x), f (m-1) + F (2m-1) > 0, find the value range of M?

∵f(m-1)+f(2m-1)>0∴f(m-1)>-f(2m-1) ∵f(-x)=-f(x)
F (m-1) > F (1-2m)
∵ the function f (x) is a decreasing function on R
∴m-1

It is known that there are exactly three real numbers a whose function f (x) = x3-ax2-1 (0 ≤ a ≤ M0) has integer zeros

a=(x^3-1)/x^2=x-1/x^2,
Because a > = 0, x > = 1,
When x = 1, a = 0
When x = 2, a = 2-1 / 4 = 7 / 4
When x = 3, a = 3-1 / 9 = 26 / 9
When x = 4, a = 4-1 / 16 = 63 / 16
x> When x = 1 increases, X-1 / x ^ 2 increases monotonically
Since there are only three a values, 26 / 9=

Given that the intersection of the positive scale function y = (2m-1) x and the inverse scale function y = 3 − MX is in the first and third quadrants, then the value range of M is______ ．

If the intersection of positive scale function y = (2m-1) x and inverse scale function y = 3 − MX is in the first and third quadrants, then 2m − 1 ＞ 03 − m ＞ 0 can be obtained, and 12 ＜ m ＜ 3 can be obtained by solving the system of inequalities

Given that the intersection of the positive scale function y = (2m-1) x and the inverse scale function y = 3 − MX is in the first and third quadrants, then the value range of M is______ ．

If the intersection of positive scale function y = (2m-1) x and inverse scale function y = 3 − MX is in the first and third quadrants, then 2m − 1 ＞ 03 − m ＞ 0 can be obtained, and 12 ＜ m ＜ 3 can be obtained by solving the system of inequalities

Given the linear function y = (2m + 4) x + 3-N, when m is in what range, the value of function y decreases with the increase of independent variable x?

2m + 4 greater than 0

Given the function y = (2m + 3) x + M-1, if the value y of the function decreases with the increase of the independent variable x, the value range of M is obtained?

y=(2m+3)x+m-1,
If the value y of the function decreases with the increase of the independent variable x,
So the coefficient of X is 2m + 3