1. Inverse of the Function $f(x) = 3x - 2$

Step 1: Find the inverse of the function.

To find the inverse, swap $x$ and $y$ and solve for $y$.

$y = 3x - 2$

Swap $x$ and $y$:

$x = 3y - 2$

Now, solve for $y$:

$x + 2 = 3y$

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

So, the inverse function is:

[ f^{-1}(x) = \frac{x