Answer
$\{(x,y)\in \mathbb{R}^{2}\ \ |\ \ $ $y\geq x+2$ $\}$
Work Step by Step
$f$ is defined when the radicand is nonnegative,
$y-x-2\geq 0$
$y\geq x+2$
This region is bordered by the line $y=x+2$ (which is included in the region).
The test point (0,0) does not satisfy the inequality, so the domain is:
the half-plane above (and including) the line $y=x+2$
or, in set notation, $\{(x,y)\in \mathbb{R}^{2}\ \ |\ \ $ $y\geq x+2$ $\}$
