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Inverse of this function in slpoe intervept form

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 \( y = x \).

Inverse of this function in slope-intercept form

Learn how to find the inverse of the linear function f(x) = -x + 6, following step-by-step instructions. This problem involves key algebraic concepts such as slope-intercept form and inverse functions. Suitable for students in Grades 9-12.

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