Answer
$ f^{-1}(x)=\frac{x-2}{3}$
Work Step by Step
We are given the function, $f(x)=3x+2$. First, we must replace $f(x)$ with y.
$y=3x+2$
Next, interchange x and y.
$x=3y+2$
Next, solve for y by subtracting 2 from both sides.
$3y=x-2$
Divide both sides by 3.
$y=\frac{x-2}{3}$
Finally, replace y with $f^{-1}(x)$.
$ f^{-1}(x)=\frac{x-2}{3}$
