设f(x)=(e^x+1)/(e^x-1),求其反函数.
问题描述：
设f(x)=(e^x+1)/(e^x-1),求其反函数.
答
y=f(x)=(e^x+1)/(e^x-1)
y-1=(e^x+1)/(e^x-1)-1=2/(e^x-1)
e^x-1=2/(y-1)
e^x=2/(y-1)+1=(y+1)/(y-1)
反函数则e^y=(x+1)/(x-1)
所以是y=ln[(x+1)/(x-1)],(x1