Find the value of x for which following expression are defined: $\frac{1}{\sqrt{x-|x|}}$

So, $\frac{1}{\sqrt{x-|x|}}$ is not defined for any $x∈R$

$x-|x|=\left\{\begin{matrix}x-x=0,\,if\,x≥0\\x+x=2x,\,if\,x<0\end{matrix}\right.$

$⇒x-|x|≤0$, for all x

Thus, $\frac{1}{\sqrt{x-|x|}}$ does not take real value for any $x∈R$ 

So, $\frac{1}{\sqrt{x-|x|}}$ is not defined for any $x∈R$