Let's solve the problem of finding the inverse of the given function.

The function provided is:

$f(x) = 8x$

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

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

$y = 8x$

2. Swap $x$ and $y$ to find the inverse:

$x = 8y$

3. Solve for $y$:

$y = \frac{x}{8}$

Thus, the inverse function is:

$f^{-1}(x) = \frac{x}{8}$

Now, let’s match this with the provided answer choices:

• A. 8
• B. $x$
• C. $8 - x$
• D. $x + 8$
• E. $\frac{x}{8}$

The correct answer is:

E. $\frac{x}{8}$

Would you like more details or have any questions?

Here are some related questions you might be interested in:

1. What are the general steps for finding the inverse of a function?
2. How do you verify if two functions are inverses of each other?
3. What are the conditions for a function to have an inverse?
4. How can we determine if a function is one-to-one?
5. How do graphical transformations affect the inverse function?

Tip: To verify that a function and its inverse are correct, substitute $f(f^{-1}(x))$ and $f^{-1}(f(x))$ and check if you get $x$.