求y=ln(x+1)/(x-1)的反函数!

题目

求y=ln(x+1)/(x-1)的反函数!

答案

(x+1)/(x-1)=e^y
(x+1)/(x-1)-1=e^y-1
2/(x-1)=e^y-1
x-1=2/(e^y-1)
x=(e^y+1)/(e^y-1)
反函数y=(e^x+1)/(e^x-1)