The given function is $f(x) = -x + 6$.

To find the inverse of this function, follow these steps:

1. Start by replacing $f(x)$ with $y$: $y = -x + 6$

2. Swap $x$ and $y$ (since finding the inverse means swapping the input and output): $x = -y + 6$

3. Solve for $y$: $x - 6 = -y$ $y = 6 - x$

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

The inverse function is in slope-intercept form, $f^{-1}(x) = -x + 6$, where the slope is $-1$ and the y-intercept is $6$.

Would you like more details or have any questions?

Here are 5 related questions you might find useful:

1. What is the geometric interpretation of the inverse function?
2. How do we verify if two functions are inverses of each other?
3. How does the slope of a function compare with its inverse?
4. What are the domain and range of both the original and inverse functions?
5. How does the line $y = x$ relate to a function and its inverse?

Tip: When graphing a function and its inverse, both should be symmetrical around the line $y = x$.