To find the inverse of the function $y = 3x - 8$, we follow these steps:

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

We start with: $y = 3x - 8$ We replace $y$ with $f(x)$: $f(x) = 3x - 8$

Step 2: Switch $x$ and $y$

Now, to find the inverse, switch the roles of $x$ and $y$: $x = 3y - 8$

Step 3: Solve for $y$

Now, solve for $y$ (this will give us the inverse function): $x + 8 = 3y$ $y = \frac{x + 8}{3}$

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

Conclusion:

The inverse function of $y = 3x - 8$ is $f^{-1}(x) = \frac{x + 8}{3}$.

Would you like more details or have any other questions?

Here are 5 related questions to expand your understanding:

1. What is the general process for finding the inverse of a function?
2. How do we verify that two functions are inverses of each other?
3. What happens if the function is not one-to-one? Can we still find an inverse?
4. How do we interpret the inverse function graphically?
5. What are real-life applications of inverse functions?

Tip: Always check if a function is one-to-one (passes the horizontal line test) before trying to find its inverse.