#### Answer

Domain: $(-\infty,\ \frac{7}{3}]$

#### Work Step by Step

We are given:
$g(x)=\sqrt{7-3x}$
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:
$7-3x \geq 0$
$7\geq 3x$
$\frac{7}{3}\geq x$
$x\leq\frac{7}{3}$
Therefore, the domain is: $(-\infty,\ \frac{7}{3}]$