Answer
$f^{-1}(x)=5x+2$
Work Step by Step
Replace $f(x)$ by $y$ to have:
$y=\dfrac{x-2}{5}$
Interchange $x$ and $y$ then solve for $y$ to have:
$x = \dfrac{y-2}{5}
\\5x= y-2
\\5x+2=y
\\y=5x+2$
Replace $y$ with $f^{-1}(x)$ to have:
$f^{-1}(x)=5x+2$
