Answer
Domain $(-\infty,-2)\cup(2,+\infty)$
Work Step by Step
We are given:
$g(x)=\sqrt x^{2}-4$
The domain of a function consists of all values that x is allowed to have. In this case, we can not take the square root of a negative number, so:
$x^{2}-4\geq0$
$(x-2)(x+2)\geq0$
$x\geq2$ or $x\geq-2$
Thus the domain is $(-\infty,-2)\cup(2,+\infty)$