Answer
The domain is the set of real numbers less than or equal to $0$.
Work Step by Step
The given function is
$y=\sqrt{-\frac{1}{2}x}+1$
The radicand cannot be negative.
So, $-\frac{1}{2}x$ is greater than or equal to zero.
$\Rightarrow -\frac{1}{2}x\geq 0$
Multiply each side by $-2$ and reverse the inequality symbol.
$\Rightarrow x\leq 0$
Hence, the domain is the set of real numbers less than or equal to $0$.
