Let's find the inverse function of $f(x) = \frac{x}{2}$.

To find the inverse, we need to solve for $x$ in terms of $y$ (where $y = f(x)$):

1. Start with the equation: $y = \frac{x}{2}$

2. Now, solve for $x$: $x = 2y$

3. Since we are finding the inverse, replace $y$ with $x$ (the variable for the inverse function): $f^{-1}(x) = 2x$

So the correct inverse function is $f^{-1}(x) = 2x$.

Answer:

The inverse function is $f^{-1}(x) = 2x$.

Would you like more explanation on inverse functions or have any other questions? Here are some related questions you may find interesting:

1. How do we verify the correctness of an inverse function?
2. How do we find the inverse of a function that involves powers or square roots?
3. What does the graph of a function and its inverse look like?
4. How can we determine if a function is one-to-one, and why does it matter for finding an inverse?
5. What is the composition of a function and its inverse? How do we prove they are inverses?

Tip: To check if two functions are true inverses, try composing them (i.e., $f(f^{-1}(x)) = x$ and $f^{-1}(f(x)) = x$)!