Y = f (x) is a decreasing function in [- 2,1], and f (A & # 178; - 1) > F (1-A) is the range of A

Y = f (x) is a decreasing function in [- 2,1], and f (A & # 178; - 1) > F (1-A) is the range of A

There is a definition field, so, - 2 ≤ A & # 178; - 1 ≤ 1, and - 2 ≤ 1-A ≤ 1, and because it is a decreasing function, so a & # 178; - 1 < 1-A, the answer is: 0 "a < 1. For reference only
Judge the parity of the following functions: (1) 1 / 3 power of y = x (2) 2 / 3 power of y = x (3) 2 / 2 power of y = x (4) 1 / 2 power of y = X
(5) Y = 2 / 3 power of X
(1) Odd functions (2) even functions (3) even functions (4) and (5) are not odd or even, and the domain of definition is not symmetric about the origin
The function y = f (x) is a decreasing function on (- 1,1) and an odd function satisfying f (a2-a-1) + F (A-2) > 0. Try to find the range of A
From the topic meaning, f (a2-a-1) + F (A-2) > 0, that is, f (a2-a-1) > F (A-2), and the function y = f (x) is odd, so f (a2-a-1) > F (2-A), and the function y = f (x) is a decreasing function on (- 1, 1), so there is − 1 < A2 − a − 1 < 1 − 1 < a − 2 < 1A2 − a − 1 < 2 − a, {− 1 < a < 0 or 1 < a < 21 < a < 3 − 3 < a < 3} 1 < a < 3, so the value range of a is {1 < a < 3 Yes (1, 3)
Finding the parity of function f (x) = 1 / (x-1 of 3) + 1 / 2
The domain of definition is x ≠ 0, which is symmetric about the origin
F (- x) = 1 / (the (- x) power of 3-1) + 1 / 2 = 3 ^ X / (1-3 ^ x) + 1 / 2
=-1+1/(1-3^x)+1/2=-1/2-1/(3^x-1)=-(1/2+1/(3^x-1))=-f(x)
So f (x) is an odd function
It is known that the function y = f (x) is a decreasing function on (0, + ∞). Try to compare the relationship between F (3 / 4) and f (A & # 178; - A + 1)
a^2-a+1-3/4=a^2-a+1/4=(a-1/2)^2>=0
So (a ^ 2-A + 1) > = 3 / 4
So f (a ^ 2-A + 1)
Since y = f (x) is a decreasing function on (0, + ∞), it shows that if x is in the range of (0, + ∞), the larger x is, the smaller y is
This problem is transformed into the problem of the ratio of 3 / 4 and a & # - A + 1
A & # 178; - A + 1 is a parabolic function with an opening upward, and the minimum value can be obtained
If the minimum is greater than 3 / 4
The problem is solved
Since y = f (x) is a decreasing function on (0, + ∞), it shows that if x is in the range of (0, + ∞), the larger x is, the smaller y is
This problem is transformed into the problem of the ratio of 3 / 4 and a & # - A + 1
A & # 178; - A + 1 is a parabolic function with an opening upward, and the minimum value can be obtained
3 / 4 is greater than the minimum
The problem is solved. Put it away
Judge the parity of the following functions y = - 3x y = x & # 178; + 10 y = x & # 178; - 1 / X & # 179; y = x & # 178; / x + 1
1. Using the domain of definition to judge the function y = x & # 178; - 1 2. Given that the function y = f (x) is odd on R and f (- 1) = 5, find the value of F (1). 3. If the function y = ax & # 178; + BX + C is odd on R, find the value of B. 4. Judge the symmetry of the image of the function y = x & # 178; + 1 / X & # 178; + 5
Even function f (x) = f (- x) odd function f (- x) = - f (x) you can judge according to this formula, there are also some non odd and non even functions. Odd function y = - 3x y = x & # 178; - 1 / X & # 179; even function y = x & # 178; + 10 non odd and non even function y = x & # 178; / x + 11 definite
The function y = f (x) is an increasing function on (- 1,1) and an odd function, which satisfies f (A & # 178; - A-1) + F (A-2) > 0. Try to find the range of A
The function y = f (x) is an increasing function on (- 1,1) and an odd function, satisfying f (A & # 178; - A-1) + F (A-2) > 0. Try to find the range of a higher than 1
f(a²-a-1) + f(a-2) ＞0
f(a²-a-1)＞-f(a-2)
-f(a-2) =f（2-a）
a²-a-1＞2-a
A ＜ - radical 3, a ＞ + radical 3
Judge the parity of the following functions: (1) f (x) = x & # 178; x 1; (2) f (x) = 2x & # 179;; (3) f (x)
Judge the parity of the following functions: (1) f (x) = x & # 178; X-1; (2) f (x) = 2x & # 179; (3) f (x) = 2x; (4) f (x) = X-1
 
If f (x) = - x2 + 2mx and G (x) = m / x + 1 are both decreasing functions in the interval [1.2], the value range of M is obtained
F (x) = - x ^ 2 + 2mx = - (x-m) ^ 2 + m ^ 2
It is a decreasing function in the interval [1.2]
That is, the axis of symmetry x = m ≤ 1
On the interval [g] = 1
That is, M > 0
So 0
Judge the parity f (x) = 3x f (x) = - 3x + 2 of the following functions