To find the inverse function of $f(x) = 3x - 5$, we need to follow these steps:

1. Replace $f(x)$ with $y$:

   $y = 3x - 5$

2. Swap $x$ and $y$ (this is because the inverse function reverses the roles of input and output):

   $x = 3y - 5$

3. Solve for $y$:

   $x + 5 = 3y$

   $y = \frac{x + 5}{3}$

4. Replace $y$ with $f^{-1}(x)$ to denote the inverse function:

   $f^{-1}(x) = \frac{x + 5}{3}$

Thus, the inverse function is:

$f^{-1}(x) = \frac{x + 5}{3}$

Would you like further details or explanations on any step?

Here are 5 related questions to explore:

1. How do you check if two functions are inverses of each other?
2. What is the domain and range of $f^{-1}(x) = \frac{x + 5}{3}$?
3. What happens if a function isn't one-to-one? Can it have an inverse?
4. How would the process change for a more complicated linear function?
5. How do inverse functions relate to graphing?

Tip: When finding the inverse, always swap the variables and then solve for the new output.