#### Answer

$(4, +\infty)$

#### Work Step by Step

(i) The denominator cannot be equal to zero thus,
$\sqrt{x-4}\ne 0
\\x-4 \ne 0^2
\\x-4 \ne 0
\\x \ne 4$
(ii) The radicand (number inside the square root symbol) cannot be negative. Thus,
$x- 4 \ge 0
\\x \ge 4$
This means that the value of $x$ has to be greater than four.
Therefore, the domain of the function is:
$(4, +\infty)$