To find the inverse of the function $f(x) = x + 3$, follow these steps:

1. Rewrite the function: $y = x + 3$

2. Express $x$ in terms of $y$: $y = x + 3$ Subtract 3 from both sides: $y - 3 = x$

3. Swap $x$ and $y$ to find the inverse function: $x = y - 3$

Thus, the inverse function $f^{-1}(x)$ is: $f^{-1}(x) = x - 3$

Would you like more details on this process or have any other questions?

Here are 8 related questions that expand on this topic:

1. What is the domain and range of the inverse function $f^{-1}(x) = x - 3$?
2. How do you verify that $f(x)$ and $f^{-1}(x)$ are indeed inverses of each other?
3. How would the process of finding the inverse change if the function were $f(x) = x - 3$?
4. What is the graphical interpretation of finding the inverse of a function?
5. How can you determine if a function is one-to-one and thus has an inverse?
6. What are the properties of a function and its inverse regarding their compositions?
7. How does the horizontal line test relate to finding the inverse of a function?
8. What are some practical applications of inverse functions in real life?

Tip: When finding an inverse function, always double-check by composing the original function and its inverse. The result should be the identity function: $f(f^{-1}(x)) = x$ and $f^{-1}(f(x)) = x$.