To find the inverse function $f^{-1}(x)$ of the function $f(x) = x + 3$, follow these steps:

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

$y = x + 3$

Step 2: Swap $x$ and $y$ to find the inverse.

$x = y + 3$

Step 3: Solve for $y$.

$y = x - 3$

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

Final Answer:

$f^{-1}(x) = x - 3$

Would you like more details on this, or do you have another question?

Here are some related questions you might find helpful:

1. How do we check if a function and its inverse are correct?
2. What is the relationship between a function and its inverse graphically?
3. How do you find the inverse of a more complex function (e.g., quadratic)?
4. What happens if a function does not have an inverse?
5. How do you find the inverse of a piecewise function?

Tip: To quickly check your inverse, compose $f(x)$ with $f^{-1}(x)$ and see if you get back $x$.