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The function given is \( f(x) = x + 8 \). To find the inverse function, denoted by \( f^{-1}(x) \), we follow these steps:

### Steps to find the inverse:
1. Start with the equation \( y = f(x) \), which means \( y = x + 8 \).
2. To find the inverse, swap \( x \) and \( y \) to represent the inverse relationship: 
   \[
   x = y + 8
   \]
3. Solve for \( y \):
   \[
   y = x - 8
   \]
   
Thus, the inverse function is:
\[
f^{-1}(x) = x - 8
\]

Would you like more details or have any questions?

Here are some related questions to explore further:
1. What is the domain of the inverse function \( f^{-1}(x) \)?
2. How do you verify that \( f(f^{-1}(x)) = x \)?
3. How would the graph of \( f(x) = x + 8 \) look compared to its inverse?
4. What is the effect of shifting the function \( f(x) = x + 8 \) by adding or subtracting constants?
5. Can you find the inverse of more complex functions like \( f(x) = 2x + 8 \)?

**Tip:** When finding the inverse of a function, always solve for the original variable after swapping \( x \) and \( y \).

f(x) = x + 8. Work out an expression for f⁻¹(x).

Learn how to find the inverse of the linear function f(x) = x + 8. This step-by-step guide explains how to derive f⁻¹(x) = x - 8, a key concept in algebra and functions. Suitable for students in Grades 9-12.

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