We are given the function:

$f(x) = \frac{x + 6}{5}$

You are asking for the inverse of the function, denoted $f^{-1}(x)$.

To find the inverse, follow these steps:

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

$y = \frac{x + 6}{5}$

2. Swap the roles of $x$ and $y$:

$x = \frac{y + 6}{5}$

3. Solve for $y$:

Multiply both sides by 5 to eliminate the denominator:

$5x = y + 6$

Now, subtract 6 from both sides:

$y = 5x - 6$

Thus, the inverse function is:

$f^{-1}(x) = 5x - 6$

Final Answer:

$f^{-1}(x) = 5x - 6$

Would you like further explanation or have any questions about this process?

Here are some related questions to explore further:

1. How do you find the inverse of other types of functions, like quadratics or exponentials?
2. What does the graph of a function and its inverse look like?
3. How do you verify that two functions are indeed inverses of each other?
4. What are the conditions for a function to have an inverse?
5. How does the concept of inverse functions apply in real-world scenarios?

Tip: Always check the domain and range of the function and its inverse to make sure the inverse is valid.