Given the function $f(x) = -x + 6$, we need to find its inverse function in slope-intercept form, which has the general form $y = mx + b$.

Steps to find the inverse:

1. Replace $f(x)$ with $y$: $y = -x + 6$

2. Swap $x$ and $y$: To find the inverse, we switch the roles of $x$ and $y$. $x = -y + 6$

3. Solve for $y$: Rearrange the equation to isolate $y$. $x - 6 = -y$ Multiply both sides by $-1$ to solve for $y$. $y = -(x - 6) = -x + 6$

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

In this case, the inverse function turns out to be the same as the original function.

Do you have any questions or would you like more details?

Here are some related questions to explore:

1. What is the general process for finding the inverse of a linear function?
2. How can you verify that two functions are inverses of each other?
3. What happens to the slope and y-intercept when finding the inverse of a linear function?
4. How does the graph of a function compare to its inverse?
5. Can all functions have an inverse? If not, why?

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