To find the inverse of the function \( f(x) = \frac{x}{2} + 2 \), follow these steps:

1. **Replace \( f(x) \) with \( y \):**
   \[
   y = \frac{x}{2} + 2
   \]

2. **Swap \( x \) and \( y \):**
   \[
   x = \frac{y}{2} + 2
   \]

3. **Solve for \( y \):**
   \[
   x - 2 = \frac{y}{2}
   \]
   \[
   y = 2(x - 2)
   \]
   \[
   y = 2x - 4
   \]

4. **Replace \( y \) with \( f^{-1}(x) \):**
   \[
   f^{-1}(x) = 2x - 4
   \]

So, the inverse function of \( f(x) = \frac{x}{2} + 2 \) is \( f^{-1}(x) = 2x - 4 \).

Would you like more details or have any questions?

Here are 5 related questions to explore further:
1. What is the inverse function of \( f(x) = \frac{x}{3} + 5 \)?
2. How do you verify that two functions are inverses of each other?
3. What is the inverse of a quadratic function, such as \( f(x) = x^2 + 3 \)?
4. How does the graph of a function compare to the graph of its inverse?
5. What are the conditions for a function to have an inverse?

**Tip:** Always remember that the inverse of a function, when composed with the original function, should return the input value (i.e., \( f(f^{-1}(x)) = x \) and \( f^{-1}(f(x)) = x \)).

Discover how to find the inverse function of f(x) = x/2 + 2 with a step-by-step solution. This problem covers the concept of inverse functions and equations, suitable for students in Grades 10-12.

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