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.
答
∵奇函数f(x)满足f(x+2)=f(x),∴周期为2,f(-x)=-f(x),
∴f(log215)=f(log
)=-f(
215 16
)=-2log
log
216 15
=2log
216 15
−8,
152
故:f(log215)的值为=2log
−8,
152