Answer
$f^{-1}(x)=\dfrac{x-2}{5}$
Work Step by Step
The given function, $
f(x)=5x+2
,$ is equivalent to
\begin{array}{l}\require{cancel}
y=5x+2
.\end{array}
Interchanging the $x$ and $y$ variables, and then solving for $y$ result to
\begin{array}{l}\require{cancel}
x=5y+2
\\\\
x-2=5y
\\\\
\dfrac{x-2}{5}=y
\\\\
y=\dfrac{x-2}{5}
.\end{array}
Hence, the inverse function is $
f^{-1}(x)=\dfrac{x-2}{5}
$.
