Answer
$f^{-1}(x),$ is $f^{-1}(x)=\dfrac{x-4}{3}$.
Work Step by Step
Let $y=f(x).$ Then the given function, $f(x)=3x+4,$ becomes $y=3x+4.$
To get the inverse, interchange the $x$ and $y$ variables and then solve for $y.$ That is,
\begin{align*}\require{cancel}
x&=3y+4
&(\text{interchange $x$ and $y$})
\\
x-4&=3y
\\\\
\dfrac{x-4}{3}&=\dfrac{\cancel3y}{\cancel3}
\\\\
\dfrac{x-4}{3}&=y
\\\\
y&=\dfrac{x-4}{3}
.\end{align*}Hence, the inverse, $f^{-1}(x),$ is $f^{-1}(x)=\dfrac{x-4}{3}$.
