Question

The range of the function $f\left(x\right)=\frac{x+2}{\left|x+2\right|}$ is __________ .

Answer 1

$\begin{array}{rcl}f\left(x\right)& =& \frac{x+2}{\left|x+2\right|}\\ & =& \left\{\begin{array}{l}\frac{x+2}{x+2};x\ge -2\\ \frac{x+2}{-\left(x+2\right)};x<-2\end{array}\right.\\ \mathrm{i}.\mathrm{e}f\left(x\right)& =& \left\{\begin{array}{l}1;x\ge -2\\ -1;x<-2\end{array}\right.\end{array}$

∴ Range of function f(x) is {−1, 1}