Answer
Domain is all real numbers greater than $4$.
In set notation, $\left\{x|x\gt4\right\}$.
Work Step by Step
Given $f(x)=\dfrac{x}{\sqrt {x−4}}$
The square root of negative numbers are imaginary numbers.
Also, division of $0$ is not allowed.
Hence, the expression inside the radical sign of the denominator cannot be negative nor be zero.
Thus,
$x−4\gt0$
$x-4+4\gt0+4$
$x\gt4$
Therefore, the domain is {$x|x\gt4$}.
