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.

Learn how to find the inverse of the linear function f(x) = 8x + 16. This detailed solution explains the concept of inverse functions, using algebraic manipulation to derive the inverse formula f^{-1}(x) = (x - 16)/8. Suitable for Grades 9-11.

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