设函数f(x)是定义在R上的奇函数,且f(2)=0,f(x)在0,1上单调递增,在（1,正无穷）上单调递减,则不等式f(x)大于等于0的解集为?

Question

设函数f(x)是定义在R上的奇函数,且f(2)=0,f(x)在【0,1】上单调递增,在（1,正无穷）上单调递减,则不等式f(x)大于等于0的解集为?

Answer 1

因为 f(x) 奇函数,所以,当x∈(0,1) 时.
f(x)= -2^(-x)
log2(5)＞log2(4)=2,
log2(5)＜log2(8)=3,
所以,0＜log2(5)-2＜1,
由f(x+2)=f(x)知,f(x)周期为2,
所以,f(log2(5))=f(log2(5)-2)
= -2^[-log2(5)+2]
= -{2^[log2(5)]}^(-1)·2^2
= -5^(-1) · 4
= -4/5