If f(x)=x−1x+1f(x) = \frac{x-1}{x+1}f(x)=x+1x−1, find f−1(x)f^{-1}(x)f−1(x).
1+x1−x\frac{1+x}{1-x}1−x1+x
1−x1+x\frac{1-x}{1+x}1+x1−x
x−1x+1\frac{x-1}{x+1}x+1x−1
x+1x−1\frac{x+1}{x-1}x−1x+1