#### Answer

$(-\infty,\ \infty)$

#### Work Step by Step

We are given:
$g(x)=\sqrt{x^{2}+9}$
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:
$x^2+9\geq0$
This is true for all values of $x$.
Thus the domain is: $(-\infty,\ \infty)$