To find the inverse of the function $f(x) = 3x - 1$, follow these steps:

1. Replace $f(x)$ with $y$:
   $y = 3x - 1$

2. Swap $x$ and $y$ (this is the step to start finding the inverse):
   $x = 3y - 1$

3. Solve for $y$ (this will give the inverse function): $x + 1 = 3y \quad \text{(add 1 to both sides)}$ $y = \frac{x + 1}{3} \quad \text{(divide both sides by 3)}$

So, the inverse function is: $f^{-1}(x) = \frac{x + 1}{3}$

Would you like more details or further explanation?

Here are 5 related questions for you to explore:

1. How do you verify that two functions are inverses of each other?
2. What is the inverse of $f(x) = 4x + 5$?
3. How do inverse functions relate to their graphs?
4. What is the domain and range of the inverse function $f^{-1}(x)$?
5. Can all functions have inverses?

Tip: For a function to have an inverse, it must be one-to-one (i.e., it must pass the horizontal line test).