The domain of the function $f(x)=\frac{1}{\sqrt{|x|-x}}$ is:

For the square root in the denominator to be defined, the expression must be strictly positive:$|x|-x>0⟹|x|>x$.For $x\ge 0$, $|x|=x$, so $x>x$ is false.For $x<0$, $|x|=-x$, so $-x>x⟹0>2x$, which is true for all $x<0$.Domain is $(-\infty ,0)$.