Question

已知定义在R上的奇函数f(x)满足f(x+2)=-f(x)，当 x属于（0，1）时，f(x)=2的x次方，则f(log1/2 23)=_

要详细过程的哦

Answer 1

f(x+4)=-f(x+2)=f(x)知f(x)为周期为4的函数
f(log1/2 23)=f((log1/2 23)+4)=f(log1/2 23/16)=-f(-log1/2 23/16)=-f(log2 23/16)
而0<(log2 23/16)<1
-f(log2 23/16)=-23/16

Answer 2

f(x)=-f(x+2)=f(x+4)
log1/2 23=-lg2 23 ≈-4.几
f(log1/2 23)=-f(log2 23)=-f(log2 23 -4)=23/16