#### Answer

$f(x)$ and $g(x)$ are inverse functions.

#### Work Step by Step

We find the inverse of $f(x)$ by solving for $x$.
\[ y = 5x + 1 \\ \\ y-1 = 5x \\ \\ \frac{y-1}{5} = x \]
Therefore, the inverse function of $f(x)$ is $\frac{x-1}{5}$.
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 $g(x)$.