Answer
Inverse: $y=\dfrac{x-2}{3}$
The inverse is a function.
Work Step by Step
To find the inverse of the given function, perform the followiong steps:
(1) Interchange $ x$ and $y$.
$$x=3y+2$$
(2) Solve for $y$.
\begin{align*}
x-2&=3y &\text{Subtract 2 from each side.}\\\\
\frac{x-2}{3}&=\frac{3y}{3} &\text{Divide 3 to both sides.}\\\\
\frac{x-2}{3}&=y
\end{align*}
Note that for $y=\dfrac{x-2}{3}$, for every value of $x$, there corresponds only one value of $y$.
Thus, the inverse of the given function is also a function.
