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 $f^{-1}(f(x)) = x$).