#### Answer

Domain: $(-\infty, \frac{1}{2}]$

#### Work Step by Step

We are given:
$f(x)=\sqrt{1-2x}$
The domain of a function consists of all values that $x$ is allowed to have. In this case, we can not take the square root of a negative number, so:
$1-2x \geq 0$
$1\geq 2x$
$\frac{1}{2}\geq x$
$ x\leq\frac{1}{2}$
Thus the domain is: $(-\infty, \frac{1}{2}]$