Given the function $f(x) = 3x - 2$, find its inverse function $f^{-1}(x)$.

1. Problem Description

Given the function $f(x) = 3x - 2$, find its inverse function $f^{-1}(x)$.

2. Solution Steps

To find the inverse of a function, we can follow these steps:

(1) Replace $f(x)$ with $y$. So, $y = 3x - 2$.

(2) Swap $x$ and $y$. So, $x = 3y - 2$.

(3) Solve for $y$ in terms of $x$.

$x = 3y - 2$

Add 2 to both sides:

$x + 2 = 3y$

Divide both sides by 3:

$y = \frac{x + 2}{3}$

(4) Replace $y$ with $f^{-1}(x)$. So, $f^{-1}(x) = \frac{x + 2}{3}$.

3. Final Answer

$f^{-1}(x) = \frac{x + 2}{3}$