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Let's solve part **b**, which asks for the inverse of the function \( f(x) = -x + 4 \).

### Steps to find the inverse of a function:

1. Start with the function \( f(x) = -x + 4 \).
2. Replace \( f(x) \) with \( y \). So, we have:
   \[
   y = -x + 4
   \]
3. Swap \( x \) and \( y \) to find the inverse. Now, it becomes:
   \[
   x = -y + 4
   \]
4. Solve for \( y \):
   \[
   x - 4 = -y
   \]
   \[
   y = -x + 4
   \]
   Thus, the inverse function is:
   \[
   f^{-1}(x) = -x + 4
   \]

In this case, the function's inverse is the same as the original function, meaning \( f(x) = f^{-1}(x) \).

Would you like a more detailed explanation or have any other questions?

Here are some related questions to deepen your understanding:
1. What is the significance of a function being its own inverse?
2. How does the graph of a function change if the inverse is the same as the function?
3. Can all linear functions have inverses? Why or why not?
4. How do you verify if two functions are inverses of each other?
5. What are the key differences in finding the inverse of a linear function versus a quadratic function?

**Tip:** When finding an inverse, always make sure the original function is one-to-one, meaning that for each \( y \) there is a unique \( x \).

Find the inverse of the function f(x) = -x + 4

Learn how to find the inverse of the linear function f(x) = -x + 4 with a clear step-by-step explanation. This problem is suitable for high school students learning about inverse functions in algebra.

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