To find the inverse function $f^{-1}(x)$ for the given function $f(x) = 3x - 8$, follow these steps:

Steps:

1. Start by replacing $f(x)$ with $y$: $y = 3x - 8$

2. Swap $x$ and $y$ to start solving for the inverse: $x = 3y - 8$

3. Solve for $y$: $x + 8 = 3y$ $y = \frac{x + 8}{3}$

4. Finally, replace $y$ with $f^{-1}(x)$: $f^{-1}(x) = \frac{x + 8}{3}$

So, the inverse function is: $f^{-1}(x) = \frac{x + 8}{3}$

Would you like further details or have any questions?

Here are 5 related questions:

1. How do you verify if a function is one-to-one (invertible)?
2. How do you check if two functions are inverses of each other?
3. What is the inverse of a quadratic function?
4. How does the inverse of a linear function compare to the original?
5. What transformations occur when taking the inverse of a function?

Tip: Always swap $x$ and $y$ when finding the inverse of a function to solve for the new variable.