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

Step 1: Switch the variables $x$ and $y$:

Since $f(x) = x + 3$, we replace $f(x)$ with $y$, so:

$y = x + 3$

Now, switch $x$ and $y$:

$x = y + 3$

Step 2: Solve for $y$:

To isolate $y$, subtract 3 from both sides:

$y = x - 3$

Final Answer:

The inverse function is:

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

Would you like me to explain why switching $x$ and $y$ gives the inverse, or how to verify the answer? Let me know!

Related Questions:

1. What is the inverse function of $f(x) = 2x + 5$?
2. How do we check if two functions are inverses of each other?
3. Why is it important to switch $x$ and $y$ when finding inverses?
4. Can all functions have inverses? If not, why?
5. How would you graph the function $f(x) = x + 3$ and its inverse?

Tip: To verify if $f^{-1}(x)$ is correct, check if $f(f^{-1}(x)) = x$ and $f^{-1}(f(x)) = x$.