Answer
The domain is {$x|x\gt4$}.
Work Step by Step
Requirement (1):
For a square root to be defined, the function inside the root must be greater than or equal to $0$.
The domain is defined by applying the requirement:
$x-4\geq0$
$x-4+4\ge 0+4$
$x\geq 4$
Requirement (2)
For a fraction to be defined, the denominator can not be equal to $0$.
The domain is defined by applying this requirement as well:
$\sqrt{x-4}\ne0$
$(\sqrt{x-4})^2\ne 0^2$
$x-4\ne0$
$x-4+4\ne 0+4$
$x\ne4$
The two requirements can be applied together, to define the domain:
$x\geq4$ and $x\ne4$
.
Therefore the domain is {$x|x\gt4$}.
