Question

Find the domain of the function
$f\left(x\right)=\frac{1}{\sqrt{|x|-x}}$

• A. $[0,\infty )$
• B. $(-\infty ,0)$
• C. $[1,\infty )$
• D. $(-\infty ,0]$

Answer 1

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

Solution:

$f\left(x\right)=\frac{1}{\sqrt{|x|-x}}$

Here, $f\left(x\right)$ is defined only when

$|x|-x>0$

or $|x|>x$

which is possible only for negative values of $x.$

Thus, the domain of $f$ will be $(-\infty ,0)$

Hence, B is the correct option.