The function given is $f(x) = x$.

To find the inverse of a function $f(x)$, we follow these steps:

1. Replace $f(x)$ with $y$: $y = x$

2. Swap $x$ and $y$ (this step reflects the function over the line $y = x$): $x = y$

3. Solve for $y$: $y = x$

Thus, the inverse of $f(x) = x$ is itself, meaning: $f^{-1}(x) = x$

This makes sense because $f(x) = x$ is a linear function with a slope of 1, and such functions are their own inverses.

Would you like any details or further clarifications on this?

---

Here are 5 related questions you might explore:

1. What is the inverse of $f(x) = 2x + 3$?
2. How do you verify if two functions are inverses of each other?
3. How would the graph of $f(x) = x$ and its inverse look?
4. What is the inverse of a quadratic function like $f(x) = x^2$?
5. What happens if a function doesn't have an inverse?

Tip: A function must be one-to-one (bijective) to have an inverse, meaning every output corresponds to exactly one input.