Answer
Domain = $\{(x,y)|-1\leq x\leq 1\quad$and$\quad -1\leq y\leq 1\}$
(see image)
Work Step by Step
Because of the restrictions for square roots, f is defined when
$ 1-x^{2}\geq 0\qquad$and$\qquad 1-y^{2}\geq 0.$
$ x^{2}\leq 1\qquad$and$\qquad y^{2}\leq 1$
$-1\leq x\leq 1\qquad$and$\qquad -1\leq y\leq 1$
This is the region inside a square in $\mathbb{R}^{2}$, sides included (the signs are $\leq$), so we use solid lines.
Domain = $\{(x,y)|-1\leq x\leq 1\quad$and$\quad -1\leq y\leq 1\}$
(see image)
