Answer
The domain is $(-\infty, -5)$ and $(-5,-3]$ and $[3,5)$ and $(5, \infty)$
Work Step by Step
Since one cannot divide by 0, the graph is not defined for
$4- \sqrt{x^2-9} = 0$
$\sqrt{x^2-9} = 4$
${\sqrt{x^2-9}}^2 = 4^2$
$x^2-9 = 16$
$x^2 = 25$
$x = \sqrt{25}$ and $x = -\sqrt{25}$
$x = 5$ and $x = -5$
Moreover, the solution of the root needs to be a real number, so the graph is not defined for
$x^2 - 9 < 0$
$x^2 < 9$
$-3 < x < 3$
So the domain is $(-\infty, -5)$ and $(-5,-3]$ and $[3,5)$ and $(5, \infty)$
