求y=ln(x+1)/(x-1)的反函数!

问题描述:

求y=ln(x+1)/(x-1)的反函数!

e的y次方=(x+1)/(x-1);
e的y次方*(x-1)=x+1;
e的y次方*x-e的y次方=x+1;
(e的y次方-1)*x=1+e的y次方;
x=(1+e的y次方)/(e的y次方-1);

(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)