Answer
$\{(x,y)\in \mathbb{R}^{2}\ \ |\ \ $ $(x-2)(x+2)(y-3)(y+3)\geq 0$ $\}$
Work Step by Step
$f$ is defined when the radicand is nonnegative,
$(x^{2}-2^{2})(y^{2}-3^{2})(y+3)\geq 0$
$(x-2)(x+2)(y-3)(y+3)\geq 0$
To graph, we draw (solid) lines$ \left\{\begin{array}{l}
x=2\\
x=-2\\
y=3\\
y=-3
\end{array}\right.$,
These four lines split the plane in 9 regions.
Taking a test point from each region, we find that
$(-4,4), (4,4), (0,0), (-4,-4)$ and $(4,-4)$
satisfy the inequality, and the others do not.
Shade regions containing the testpoints that satisfy the inequality.
Domain: $\{(x,y)\in \mathbb{R}^{2}\ \ |\ \ $ $(x-2)(x+2)(y-3)(y+3)\geq 0$ $\}$
