Show that $f : [-1,1]$ $\rightarrow R$, given by $f(x) =\frac {x } { (x+2)}$ is one-one. Find the inverse of of the $f : [-1,1] \rightarrow$ Range $f$.

Question

Hint: For $y \in R, \; f(x) = \large\frac{x}{x+2}$, for some $x \in [-1,1]$ i.e, $x = \large\frac{2y}{1-y}$