Question

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

Answer 1

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

$$\begin{gathered} f\left(x\right)=\frac{x+2}{\left|x+2\right|} \\ =\left\{\begin{array}{l}\frac{x+2}{x+2},x+2\ge 0\\ \frac{x+2}{-\left(x+2\right)},x+2<0\end{array}\right. \\ =\left\{\begin{array}{l}1,x+2\ge 0\\ -1,x+2<0\end{array}\right. \end{gathered}$$

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

Hence, the range of the function f : R –{–2) → R given by $f\left(x\right)=\frac{x+2}{\left|x+2\right|}$ is {–1, 1}.