If A=R- {+1} and function f: A →A is defined by $f(x)=\frac{x+1}{x-1}$ then $f^{-1}(x)$ is given by :

$\frac{1}{x-1}$ $\frac{1}{1-x}$ $\frac{x+1}{1-x}$ $\frac{x+1}{x-1}$

$\frac{x+1}{x-1}$