Question

If $f\left(x\right)=\frac{1}{\sqrt{|x|-x}}$, then domain of $f\left(x\right)$ is

• A. $(-\infty ,0)$
• B. $(-\infty ,2)$
• C. $(-\infty ,\infty )$
• D. None of these

Answer 1

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

Given, $f\left(x\right)=\frac{1}{\sqrt{|x|-x}}$
For $f\left(x\right)$ to be defined, $|x|>x$
$\Rightarrow x<-x,x>x$
$\Rightarrow 2x<0(\because x>x$ is not possible)
$\Rightarrow x<0$
Hence, domain of $f\left(x\right)$ is $(-\infty ,0)$.