已知奇函数f(x)满足f(x+2)=f(x),且0<x<1时,f(x)=2x,求f(log215)的值.

问题描述:

已知奇函数f(x)满足f(x+2)=f(x),且0<x<1时,f(x)=2x,求f(log215)的值.

∵奇函数f(x)满足f(x+2)=f(x),∴周期为2,f(-x)=-f(x),
∴f(log215)=f(log

 
15
16
2
)=-f(
log
16
15
2
)=-2log
 
16
15
2
=2log
  152
−8

故:f(log215)的值为=2log
  152
−8