If f(x)=2x−1x+1f(x) = \frac{2x-1}{x+1}f(x)=x+12x−1, find f−1(x)f^{-1}(x)f−1(x).
f−1(x)=x+12x−1f^{-1}(x) = \frac{x+1}{2x-1}f−1(x)=2x−1x+1
f−1(x)=x+11−2xf^{-1}(x) = \frac{x+1}{1-2x}f−1(x)=1−2xx+1
f−1(x)=x+12−xf^{-1}(x) = \frac{x+1}{2-x}f−1(x)=2−xx+1
f−1(x)=1+x2−xf^{-1}(x) = \frac{1+x}{2-x}f−1(x)=2−x1+x