Question

一道函数题

f(x)为R上偶函数，f(x)在[0,正无穷）上单调递减，f(2)=0,求满足f(2x-1)>f(1/2)的x

要具体过程

Answer 1

因为f(x)为R上偶函数，f(x)在[0,正无穷）上单调递减，

所以 f(x)在（负无穷，0】上单调递增

讨论一下
1.
2x-1大于零时

f(2x-1)>f(1/2)

因为 f(x)在[0,正无穷）上单调递减
所以 2x-1<1/2
1/2<x<3/4
2.
2x-1小于于零时

f(2x-1)>f(1/2)

因为 f(x)在（负无穷，0】上单调递增
所以 2x-1>1/2

无解

所以答案是 1/2<x<3/4