Question

已知奇函数f(x)满足f(x+2)=f(-x).当x∈(0,1)时,f(x)=2^x.求f(log0.5 18 )

Answer 1

由于：f(x)为奇函数
则有：f(-x)=-f(x)
又：f(x+2)=f(-x)=-f(x)
则令x=x+2
则有：f[(x+2)+2]=-f(x+2)
则：f(x+4)=-f(x+2)
又：f(x+2)=-f(x)
则：f(x+4)=-[-f(x)]=f(x)
2.
f[log2(1/18)]
=f[log2(1)-log2(18)]
=f[0-log2(2*9)]
=f[-log2(2)-log2(9)]
=f[-1-log2(9)]
由于；f(x)=f(x+4)
则：f(-1-log2(9))
=f[3-log2(9)]
=f[log2(2^3)-log2(9)]
=f[log2(8)-log2(9)]
=f[log2(8/9)]
由于：1/2