函数f(x)=(2^x-1)/(2^x+1) (x∈R)的反函数f^-1(x)=
问题描述：
函数f(x)=(2^x-1)/(2^x+1) (x∈R)的反函数f^-1(x)=
答
a=2^x
y-1=(a-1)/(a+1)-1=(a-1-a-1)/(a+1)=-2/(a+1)
a+1=2/(1-y)
a=2/(1-y)-1
2^x=(1+y)/(1-y)
x=log2[(1+y)/(1-y)]
所以f^-1(x)=log2[(1+x)/(1-x)],-1