Answer
Inverse: $y=\dfrac{x-7}{5}$
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 $y$.
$$x=5y+7$$
(2) Solve for $y$.
\begin{align*}
x-7&=5y &\text{Subtract 7 from each side.}\\\\
\frac{x-7}{5}&=\frac{5y}{5} &\text{Divide 5 to both sides.}\\\\
\frac{x-7}{5}&=y\\\\
\end{align*}
Note that for $y=\dfrac{x-7}{5}$, for every value of $x$, there is only one corresponding value for $y$.
Thus, the inverse of the given function is also a function.
