Question

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

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

Answer 1

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

$f\left(x\right)=\frac{2+x}{2-x},x\ne 2$

Let $f\left(x\right)=y$,

$y=\frac{2+x}{2-x}$

$2y-xy=2+x$

$2y-2=x(1+y)$

$x=\frac{2(y-1)}{1+y}$

Now consider the domain for value $x$. $y$ cannot take '-1' value as

$x$ is not defined for that value.

Hence, range will be $R-\{-1\}$