Question

The range of the function $f\left(x\right)=\frac{2+x}{2-x},x\ne 2$ is

• A. $R$
• B. $R-\{-1\}$
• C. $R-\left\{1\right\}$
• D. $R-\{-2\}$

Answer 1

The correct option is B $R-\{-1\}$

$y=\frac{2+x}{2-x}\Rightarrow 2y-yx=2+x\Rightarrow x(y+1)=2y-2\Rightarrow x=\frac{2y-2}{y+1}\Rightarrow f^{-1}\left(x\right)=\frac{2x-2}{x+1}$
$\therefore$ Range of $f=$ Domain of $f^{-1}=R-\{-1\}$