Answer
$f^{-1}(x)= \frac{1}{3}(x+2)$
Work Step by Step
We are given:
$f(x)=3x-2$
To find the inverse function, we switch $x$ and $y$ and solve for $y$:
$y=3x-2$
$x=3y-2$
$x+2=3y$
$y=\frac{x+2}{3}=\frac{1}{3}(x+2)$
Thus the inverse is:
$f^{-1}(x)= \frac{1}{3}(x+2)$
