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

1. Start with the given function: $f(x) = 8x + 16$

2. Replace $f(x)$ with $y$: $y = 8x + 16$

3. Swap $x$ and $y$ to reflect the inverse: $x = 8y + 16$

4. Solve for $y$ (which is now $f^{-1}(x)$): $x - 16 = 8y$ $y = \frac{x - 16}{8}$

So, the inverse function is: $f^{-1}(x) = \frac{x - 16}{8}$

Would you like more details on inverse functions or any specific steps? Here are some related questions:

1. How do you verify if two functions are inverses of each other?
2. What is the domain and range of $f(x) = 8x + 16$?
3. How can you graph $f(x)$ and its inverse $f^{-1}(x)$?
4. How do linear functions behave when their inverses are calculated?
5. What happens if you try to find the inverse of a non-linear function?

Tip: To check if two functions are inverses, compose them (i.e., calculate $f(f^{-1}(x))$ and $f^{-1}(f(x))$). If both compositions give $x$, the functions are inverses.