The domain of $\sqrt{\left|x\right|-x}$ is 

The given function is $f\left(x\right)=\sqrt{\left|x\right|-x}$

To get the domain of the function, the restriction is square root

Under square root value must be non negative

hence, $\left|x\right|-x\ge 0\Rightarrow \left|x\right|\ge x$

This is possible for all real numbers,

Therefore, the domain of the given function $f\left(x\right)=\sqrt{\left|x\right|-x}$ is the set of all real numbers or simply $\boxed{\left(-\infty ,\infty \right)}$