Question

If $f:x\to \frac{2x-3}{x+1},x\ne -1$, find $f^{-1}$.

Answer 1

Given, $f\left(x\right)=\frac{2x-3}{x+1}$

$\Rightarrow y=\frac{2x-3}{x+1}\Rightarrow xy+y=2x-3\Rightarrow y+3=2x-xy\Rightarrow x(2-y)=y+3\Rightarrow x=\frac{y+3}{2-y}$

Interchanging $x$ and $y$

$\Rightarrow f^{-1}\left(x\right)=\frac{x+3}{2-x}$