Question

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

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

Answer 1

Answer: (B)

We have
$f(x)=y=\frac{2+x}{2-x}$
$\Rightarrow 2 y-x y=2+x$
$\Rightarrow 2 y-2=x+x y$
$\Rightarrow 2 y-2=x(1+y)$
$\Rightarrow x=\frac{2 y-2}{1+y}$
Since, $x=\frac{2 y-2}{y+1}$ is defined if $y+1 \neq 0$ i.e. $y \neq-1$
$\therefore$ Range of $f(x)=R-\{-1\}$