Find the inverse function in slope-intercept form (mx+b):

f, of, x, equals, minus, x, plus, 6

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 \( x \).

Find the inverse function in slope-intercept form (mx+b): f(x) = -x + 6

Learn how to find the inverse of the linear function f(x) = -x + 6 in slope-intercept form. This solution covers essential algebraic concepts, including inverse functions and linear equations. Suitable for high school students (Grades 9-12).

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