#### Answer

Domain: $(4,\ \infty)$

#### Work Step by Step

We are given:
$f(x)= \frac{3}{\sqrt{x-4}}$
The domain of a function consists of all the values that $x$ is allowed to have. In this case, we can not take the square root of a negative number:
$x-4\ge 0$
$x\ge 4$
In addition, we can not have division by $0$:
$x-4\ne 0$
$x\ne 4$
Thus overall: $x\gt 4$.
Therefore, the domain is: $(4,\ \infty)$