Answer
Domain is $(−∞,−2)∪(4,+∞)$
Work Step by Step
We are given:
$g(x)=\sqrt x^{2}-2x-8$
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:
$x^{2}-2x-8\geq0$
$(x-4)(x+2)\geq0$
Thus the domain is $(−∞,−2)∪(4,+∞)$