To find the inverse function $f^{-1}(x)$ of the function $f(x) = \frac{x + 6}{5}$, follow these steps:

1. Start by setting $y = f(x)$: $y = \frac{x + 6}{5}$

2. Swap $x$ and $y$ to find the inverse: $x = \frac{y + 6}{5}$

3. Solve for $y$: $x \times 5 = y + 6 \quad \text{(Multiply both sides by 5)}$ $5x = y + 6$ $y = 5x - 6$

So, the inverse function is: $f^{-1}(x) = 5x - 6$

Do you want more details or have any questions?

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Here are five related questions:

1. How do you verify if two functions are inverses of each other?
2. What is the graphical interpretation of an inverse function?
3. How do you find the inverse of a function that is not linear?
4. Can all functions have an inverse? Why or why not?
5. How does the domain and range of a function relate to its inverse?

Tip: To verify that two functions are inverses, compose them (i.e., $f(f^{-1}(x))$ and $f^{-1}(f(x))$) and check if both simplify to $x$.