#### Answer

Domain: $(-\infty,\ 6)$

#### Work Step by Step

We are given:
$f(x)= \frac{x^{2}}{\sqrt{6-x}}$
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:
$6-x\ge 0$
$6\ge x$
$x\le 6$
In addition, we can not have division by $0$:
$6-x\ne 0$
$x\ne 6$
Therefore, the domain is: $(-\infty,\ 6)$