To solve for the inverse of the function $f(x) = \frac{x}{3}$, we need to follow these steps:

Steps to Find the Inverse Function

1. Start with the function $f(x) = \frac{x}{3}$.

2. Rewrite the function in terms of $y$:
   $y = \frac{x}{3}$

3. Swap $x$ and $y$. This is because, for the inverse function, we want to solve for $y$ in terms of $x$. So: $x = \frac{y}{3}$

4. Solve for $y$: Multiply both sides of the equation by 3 to isolate $y$: $y = 3x$

5. Write the inverse function:
   The inverse function is: $f^{-1}(x) = 3x$

Final Answer:

The inverse function of $f(x) = \frac{x}{3}$ is: $f^{-1}(x) = 3x$

Would you like a more detailed explanation, or do you have any specific questions?

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Here are 5 related questions to expand your understanding:

1. How do you find the inverse of a more complex linear function?
2. What is the geometric interpretation of a function and its inverse?
3. How can you verify that two functions are inverses of each other?
4. How do the domain and range of a function relate to its inverse?
5. Can every function have an inverse? Why or why not?

Tip: To verify if two functions are inverses, check if $f(f^{-1}(x)) = x$ and $f^{-1}(f(x)) = x$.