Question

已知f(x)是定义在(-1,1)上的偶函数，且在[0,1)为增函数，若f(a-2)-f(4-a^2)<0,则a范围为？

A(根号3，2）U（2，根号5）
B（-根号3，-1）U（1，根号3）
C（-1,1)
D(-2 , -根号3）U（根号3，2）

Answer 1

-1<x<1
f(x) = f(-x)
f(x) 在[0,1)为增函数
=> f(x) 在[-1,0)为减函数
f(a-2) is defined
=> -1< a-2< 1
1<a< 3
f(4-a^2) is defined
=> -1< 4-a^2 < 1
=> -1< 4-a^2 and 4-a^2 < 1
=> a^2 < 5 and a^2 > 3
=> -√5<a <√5 and { a> √3 or a< -√3 }
√3 < a < √5 or -√5<a< -√3
f(a-2) is defined and f(4-a^2) is defined
=> 1<a< 3 and {√3 < a <√5 or -√5<a<-√3 }
=> 1<a<√5

f(a-2)-f(4-a^2)<0
=> f(a-2) < f(4-a^2)
=> |a-2| < |4-a^2|
case1: for 1<a<2
|a-2| < |4-a^2|
-(a-2) < 4-a^2
a^2-a-2 < 0
(a-2)(a+1)>0
-1<a<2
ie 1<a<2

case 2 for 2=<a <√5
|a-2| < |4-a^2|
=> a-2 < -(4-a^2)
a^2-a+2 >0
(a-2)(a+1) >0
a>2 or a< -1
ie 2< a < √5

case 1 or case 2
1<a<2 or 2< a < √5

Answer 2

f(a-2)-f(4-a^2)<0

f(a-2)-f(2+a)（2-a）<0 （0.1）为增， （1，-1）为偶，，，

自己算啊

追问

a的平方啊。

Answer 3

自己算

Answer 4

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