Answer
$f(x)$ and $g(x)$ are inverse functions.
Work Step by Step
Let us find the inverse of $f(x)$ by solving for $x$.
\[ y = \sqrt{x-4} \\ \\ y^2 = x-4 \\ \\ y^2 + 4 = x \]
However, notice that the domain of $f(x)$ is from $[4, \infty)$. Therefore, looking at the solution graphically, there cannot be any point on $g(x)$ with a $y$ coordinate of less than 4.
Graphically, we see that every point on $f(x)$, when reflected over the line $g(x)$ lies on one point on $g(x)$. Specifically, if a point $(a,b)$ is on $f(x)$, then there is a point $(b, a)$ on $g(x)$.
