Answer
$\mathrm{Domain:}\ \ (-\infty,\infty)$
$\mathrm{See\:the\:graph\:below.}$
Work Step by Step
We can take the square root only of positive numbers. Since the absolute value of $\ x\ $ will always give positive numbers, the domain of the given function is $\ y=\sqrt{|x|}\ $ is $\ (-\infty,\infty).$
The graph of the given function $\ y=\sqrt{|x|}\ $ is similar to the graph of $\ y=\sqrt{x}\ $ when $\ x\geq0\ $, but reflects itself along the $\ \mathrm{y-axis}\ $ when $\ x<0.$
See the graph below.
