If y = f (x) is an even function and a decreasing function on [0, + ∞), then the increasing function interval of F (1-x ＾ 2) is Can you give me the detailed process? The answer is (- ∞, - 1] ∪ [0, 1] But what about the process?

If y = f (x) is an even function and a decreasing function on [0, + ∞), then the increasing function interval of F (1-x ＾ 2) is Can you give me the detailed process? The answer is (- ∞, - 1] ∪ [0, 1] But what about the process?

When x

Given that a is greater than B and greater than 0, even function y = f (x) is an increasing function on the interval [- B, - A]. The monotonicity of y = f (x) on the interval [a, b] is judged and proved

prove
Let - B ＜ x1 ＜ x2 ＜ - A
Y = f (x) is an increasing function on the interval [- B, - A]
∴f(x1)＜f(x2)
Even function
f(-x1)=f(x1)＜f(x2)=f(-x2)
∵-b＜x1＜x2＜-a
∴b＞-x1＞-x2＞a
Therefore, y = f (x) decreases on the interval [a, b]

If y = f (x) is an even function and a decreasing function on [0, + ∞), then the increasing function interval of F (1-x2) is______ .

When x ≤ - 1, y = 1-x2 is an increasing function and 1-x2 ＜ 0, so f (1-x2) is an increasing function

If y = f (x) is an even function and a decreasing function on [0, + ∞), then the increasing function interval of F (1-x2) is______ .

When x ≤ - 1, y = 1-x2 is an increasing function and 1-x2 ＜ 0, so f (1-x2) is an increasing function

The even function f (x) defined on R is a decreasing function on the interval [- 1,0]. If a and B are the two inner angles of an acute triangle, then () A. f（sinA）＞f（cosB） B. f（sinA）＜f（cosB） C. f（sinA）＞f（sinB） D. f（cosA）＜f（cosB）

∵ the even function f (x) is a minus function on the interval [- 1, 0],
ν f (x) is an increasing function on the interval [0,1]
A and B are the two inner angles of an acute triangle,
∴A+B＞π
2，A＞π
2-B，1＞sinA＞cosB＞0．
∴f（sinA）＞f（cosB）．
Therefore, a

It is known that y = f (x) is an even function, and the function is subtracted from 0 to integer infinity. The monotone interval of function f (the square of 1-x) is obtained as it was stated

First of all, because f (x) is decreasing on (0, + ∞) and even function, we can know that f (x) is increasing on (- ∞, 0). Next, if 1-x2 is greater than 0, X belongs to (- 1,1), then FX is decreasing. If 1-x2 is less than 0, X belongs to (- ∞, - 1) ∪ (1, + ∞), then FX is increasing

It is known that y = f (x) is an even function on R and an increasing function on [0,3]. For X ∈ R, f (x + 6) = f (x) + F (3) is obtained It is known that y = f (x) is an even function on R and an increasing function on [0,3]. For X ∈ R, if f (x + 6) = f (x) + F (3), find the value of F (3), and the number of real roots of f (x) = 0 on [- 9,9]

If f (x) = f (- x) x = - 3, then f (3) = f (- 3) + F (3) = 0 [0,3] increasing function has only solution 3 in [0,3] f (x) = 0

It is known that y = f (x) is an even function on R and an increasing function on (0, + ∞). If f (a ^ 2 + 3) > F (4a), find the value range of A 2 it is known that y = f (x) is an odd function on the definition domain (- 4,4) and an increasing function on (- 4,4). If (3a ^ 2 + 1) + F (4a) > 0, find the value range of A 3 it is known that y = f (x) is an odd function on the domain (- 1,1) and a decreasing function on (- 1,1). Find the value range of a if f (a ^ 2) + F (a) > 0 4 it is known that y = f (x) is an odd function on the definition domain (5. - 5) and an increasing function on (5. - 5) f (a ^ 2 + 1) + F (2a-4) > 0. Find the value range of A 5F (x) is an even function and a minus function in [0, + ∞). Compare the sizes of F (- 3) and f (a ^ 2-2a + 4)

1. If y = f (x) is an even function on R and an increasing function on (0, + ∞), then it is a decreasing function on (- ∞, 0), so a ^ 2 + 3 > | 4a|
When a > = 0, a ^ 2 + 3 > 4a, a > 3, or 0 = when a < 0, a ^ 2 + 3 > - 4A, a < - 3 or - 1, so the union sets a ∈ (- ∞, - 3) ∪ (- 1,1) ∪ (3, + ∞)
2. Y = f (x) is an odd function on the domain (- 4,4) and an increasing function on (- 4,4)
f(3a^2+1)+f(4a)>0,f(3a^2+1)>-f(4a)=f(-4a)
3a^2+1>-4a,
a> - 1 / 3 or a < - 1
Combined definition domain
3. Y = f (x) is an odd function on the domain (- 1,1) and a decreasing function on (- 1,1)
f(a^2)+f(a)>0
F (a ^ 2) > - f (a) = f (- a), a ^ 2 > - A, a > 0 or a < - 2

Given that even function f (x) defined on R satisfies f (x) = f (2-x), it is proved that f (x) is a periodic function How to prove that a function is a periodic function?

Find a t such that f (x) = f (x + T), that is, prove that the function is periodic
F (- x) = f (x) = f (2-x), t = 2

It is known that even function f (x) defined on R satisfies f (x + 2) f (x) = 1 and f (x) > 0. It is proved that f (x) is a periodic function

F (x + 2) = 1 / F (x), so f (x + 4) = f (x + 2 + 2) = 1 / F (x + 2) = f (x), so f (x) is a periodic function with period 4