Answer
$(-\infty,-7]\cup(-4,3)\cup[9,\infty)$.
Work Step by Step
The domain requirement for $f(x)=\sqrt {\frac{x^2-2x-63}{x^2+x-12}}=\sqrt {\frac{(x+7)(x-9)}{(x+4)(x-3)}}$ is $\frac{(x+7)(x-9)}{(x+4)(x-3)}\geq0$ which gives solution set $x\geq9$ (all factors are positive or with one zero), $-4\lt x\lt3$ (two factors are negative), $x\leq-7$ (all factors are negative or with one zero), in interval notation $(-\infty,-7]\cup(-4,3)\cup[9,\infty)$.
