设f(x)=1+a^x/1-a^x(a>0且a不等于1),g(x)是f(x)的反函数,求g(x)

Question

设f(x)=1+a^x/1-a^x(a>0且a不等于1),g(x)是f(x)的反函数,求g(x)

Answer 1

y=(1+a^x)/(1-a^x)
y-ya^x=1+a^x
(y+1)a^x=y-1
a^x=(y-1)/(y+1)
所以g(x)=ln[(x-1)/(x+1)],-1