Find the inverse f(x) = (x)/(x + 2)

Question

Find the inverse

f(x) =
`(x)/(x + 2)`

Answer 1

`\bf f(x)=y=\cfrac{x}{x+2}\impliedby \textit{let's switch the variables} \\\\\\ \boxed{x}=\cfrac{\boxed{y}}{\boxed{y}+2}\implies x(y+2)=y\implies xy+2x=y \\\\\\ xy-y=2x\implies y(x-1)=2x\implies y=\cfrac{2x}{x-1}\impliedby f^(-1)(x)`