Answer
$\displaystyle\{x|x\geq 0$ and $x\neq 4\}$
Work Step by Step
We know that $\displaystyle \frac{\sqrt{x}}{x^{2}-3x-4}$ is undefined whenever the denominator is 0, so:
$x^2-3x-4=(x+1)(x-4)=0$
$x=-1, x=4$
The equation is also undefined when taking the square root of a negative number ($x\lt0$).
Combining these restrictions, we get the domain:
$\{x|x\geq 0$ and $x\neq 4\}$
