Answer
Domain = $\{(x,y)|y\leq 2x\}$
(see image)
Work Step by Step
Because of the restrictions for square roots, f is defined when
$2x-y\geq 0$
that is, for (x,y) such that
$y\leq 2x.$
The $\mathbb{R}^{2}$ plane is divided into two regions by the line y=2x.
The domain contains the line (graph with solid line)
The point (1,1) satisfies the inequality, so the domain contains the region it belongs to (below the line)
Domain = $\{(x,y)|y\leq 2x\}$
(see image)
