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The given problem asks to find the inverse of the function \( f(x) = \frac{1}{2}x + 8 \).

To find the inverse of a function, we follow these steps:

### Steps to find the inverse of \( f(x) \):
1. Start with the function \( f(x) = \frac{1}{2}x + 8 \).
2. Replace \( f(x) \) with \( y \), so:  
   \[ y = \frac{1}{2}x + 8 \]
3. Swap \( x \) and \( y \) to find the inverse:  
   \[ x = \frac{1}{2}y + 8 \]
4. Solve for \( y \):
   \[
   x - 8 = \frac{1}{2}y
   \]
   \[
   y = 2(x - 8)
   \]
   \[
   y = 2x - 16
   \]
5. Thus, the inverse function is \( f^{-1}(x) = 2x - 16 \).

### The correct answer is:
\[
\boxed{E. \ f^{-1}(x) = 2x - 16}
\]

Would you like more details or have any questions?  
Here are 5 related questions:
1. How can you verify if two functions are inverses of each other?
2. What are the conditions for a function to have an inverse?
3. How do you find the inverse of a quadratic function?
4. Can a function have more than one inverse?
5. How does the graphical interpretation of inverse functions work?

**Tip**: To check if two functions are inverses, their compositions should give the identity function \( f(f^{-1}(x)) = x \) and \( f^{-1}(f(x)) = x \).

Diberikan fungsi f dari R ke R dengan rumus f(x) = (1/2)x + 8. Invers dari fungsi f adalah ....

Learn how to find the inverse function of f(x) = (1/2)x + 8 with a step-by-step explanation. This problem covers key algebraic concepts, including the calculation of inverse functions, and is suitable for students in Grades 9-12.

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