The function given is $f(x) = x + 8$. To find the inverse function, denoted by $f^{-1}(x)$, we follow these steps:

Steps to find the inverse:

1. Start with the equation $y = f(x)$, which means $y = x + 8$.
2. To find the inverse, swap $x$ and $y$ to represent the inverse relationship: $x = y + 8$
3. Solve for $y$: $y = x - 8$

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

Would you like more details or have any questions?

Here are some related questions to explore further:

1. What is the domain of the inverse function $f^{-1}(x)$?
2. How do you verify that $f(f^{-1}(x)) = x$?
3. How would the graph of $f(x) = x + 8$ look compared to its inverse?
4. What is the effect of shifting the function $f(x) = x + 8$ by adding or subtracting constants?
5. Can you find the inverse of more complex functions like $f(x) = 2x + 8$?

Tip: When finding the inverse of a function, always solve for the original variable after swapping $x$ and $y$.