若函数f(x)是偶函数,在x∈[0,+∞)上单调减,且f(2)=0,则不等式f(log1/2 x)≤0

问题描述:

若函数f(x)是偶函数,在x∈[0,+∞)上单调减,且f(2)=0,则不等式f(log1/2 x)≤0

函数f(x)是偶函数,在x∈[0,+∞)上单调减
∴在(-∞,0]递增
[想象y=-x^2]
f(2)=0
f(log1/2 x)≤0
∴log1/2(x)≤-2或log1/2(x)≥2
0