已知f(x)=log(1/2)x,则不等式[f(x)]^2>f(x^2)的解集为
问题描述：
已知f(x)=log(1/2)x,则不等式[f(x)]^2>f(x^2)的解集为
答
令t=log(1/2)x (x>0)
原不等式等价于
t^2>2t
即 t2
==> log(1/2)x
因为底数0.51
答
f(x)=log(1/2)x
[f(x)]^2>f(x^2)
[log(1/2)x]^2>log(1/2)x^2=2log(1/2)x
令log(1/2)x=a
a^2>2a
a^2-2a>0
a(a-2)>0
a2
log(1/2)x1
log(1/2)x>2=log(1/2)1/4
0