Question

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

• A. $\frac{2x}{(1+x)}$
• B. $\frac{-2x}{(1-x)}$
• C. $\frac{2x}{(1-x)}$
• D. $\frac{x}{(1-x)}$

Answer 1

The correct option is C $\frac{2x}{(1-x)}$

$y=\frac{x}{x+2}$
$\Rightarrow xy+2y=x$
$\Rightarrow 2y=x(1-y)$
$\Rightarrow x=\frac{2y}{1-y}$
$\therefore$Inverse of function$=\frac{2x}{1-x}$