# The range of the function f : R –{–2) → R given by

Question:

The range of the function $f: R-\{-2) \rightarrow R$ given by $f(x)=\frac{x+2}{|x+2|}$ is _________.

Solution:

Given: $f(x)=\frac{x+2}{|x+2|}$

$f(x)=\frac{x+2}{|x+2|}$

$= \begin{cases}\frac{x+2}{x+2} & , x+2 \geq 0 \\ \frac{x+2}{-(x+2)} & , x+2<0\end{cases}$

$= \begin{cases}1 & , x+2 \geq 0 \\ -1 & , x+2<0\end{cases}$

To find the range, we find the real values of y obtained.

Hence, the range of the function $f: R-\{-2) \rightarrow R$ given by $f(x)=\frac{x+2}{|x+2|}$ is $\{-1,1\}$