Answer
$f(x)$ and $g(x)$ are inverse functions.
Work Step by Step
Let us find the inverse of $f(x)$ by solving for $x$.
\[ y = 3-4x \\ \\ y-3 = -4x \\ \\ \frac{y-3}{-4} = x \\ \\ \frac{3-y}{4} = x \]
Therefore, the inverse function of $f(x)$ is $\frac{3-x}{4}$, which is $g(x)$.
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 $g(x)$.
