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To find the inverse of the given function \( f(x) = x + 4 \), follow these steps:

1. **Replace \( f(x) \) with \( y \):**
   \[
   y = x + 4
   \]

2. **Swap \( x \) and \( y \):**
   \[
   x = y + 4
   \]

3. **Solve for \( y \):**
   Subtract 4 from both sides:
   \[
   y = x - 4
   \]

4. **Replace \( y \) with \( f^{-1}(x) \):**
   \[
   f^{-1}(x) = x - 4
   \]

### Final Answer:
\[
f^{-1}(x) = x - 4
\]

Let me know if you'd like further clarification or additional examples!  

Here are 5 related questions you can explore:
1. How can you verify that \( f(x) \) and \( f^{-1}(x) \) are inverses of each other?
2. What are the domain and range of \( f(x) = x + 4 \) and its inverse?
3. How does the graph of \( f(x) = x + 4 \) compare to its inverse \( f^{-1}(x) \)?
4. Can all functions have inverses? Why or why not?
5. How does the concept of one-to-one functions relate to invertibility?

**Tip:** To check your inverse, substitute \( f(f^{-1}(x)) = x \) or \( f^{-1}(f(x)) = x \). This confirms the functions are true inverses.

The function f(x) = x + 4 is one-to-one. Find an equation for f⁻¹(x), the inverse function.

Learn how to find the inverse of the function f(x) = x + 4 with a step-by-step solution. This guide explains key algebraic concepts and the inverse function property, suitable for students in Grades 9-11.

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