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The given function is:

\[
f(x) = \frac{8}{x + 5}
\]

To find the inverse function, follow these steps:

### Step-by-Step Solution:

1. **Write \( y = f(x) \)**:
   \[
   y = \frac{8}{x + 5}
   \]

2. **Swap \( x \) and \( y \)**:
   \[
   x = \frac{8}{y + 5}
   \]

3. **Solve for \( y \)**:
   \[
   x(y + 5) = 8
   \]
   \[
   xy + 5x = 8
   \]
   \[
   xy = 8 - 5x
   \]
   \[
   y = \frac{8 - 5x}{x}
   \]

4. **Thus, the inverse function is**:
   \[
   f^{-1}(x) = \frac{8 - 5x}{x}
   \]

Would you like more details or have any questions? Here are five related questions you might find useful:

1. How can you verify that two functions are inverses of each other?
2. What is the domain and range of the inverse function \( f^{-1}(x) \)?
3. What transformations are involved when finding the inverse of a function like this?
4. How do the vertical asymptotes of \( f(x) \) and \( f^{-1}(x) \) compare?
5. How would you graph the original function and its inverse on the same coordinate plane?

**Tip:** Always check the domain restrictions of the original function to ensure the inverse function is correctly defined.

Learn how to find the inverse function of f(x) = 8/(x + 5) with a detailed step-by-step solution. This problem covers the concept of inverse functions in calculus and algebra, suitable for advanced high school students in Grades 11-12.

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