Question

The domain of $f\left(x\right)=\frac{\left|x\right|}{x}$ is

• A. $(-\infty ,\infty )$
• B. $(-\infty ,0)\cup (0,\infty )$
• C. $(-2,2)$
• D. $(-3,3)$

Answer 1

The correct option is B $(-\infty ,0)\cup (0,\infty )$

$f\left(x\right)=\{\begin{array}{ccc}1,& x>0& \\ -1,& x<0& \end{array}$
$\therefore$ $f$ is not defined at $0$
$\therefore$ domain of $f$ is $(-\infty ,0)\cup (0,\infty )$