The domain of the function

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

f(x) is defined if |x| − x > 0

i.e |x| > x

i.e x < |x| 

which is possible for negative real numbers

$\therefore$ Domain for $f(x)$ is $\mid R^{-} \sim\{0\}$