To find the inverse of the function $f(x) = 2x + 1$, we need to follow these steps:

1. Replace $f(x)$ with $y$: $y = 2x + 1$

2. Swap $x$ and $y$: This step helps in finding the inverse function. $x = 2y + 1$

3. Solve for $y$: Isolate $y$ on one side of the equation. $x - 1 = 2y$ $y = \frac{x - 1}{2}$

4. Replace $y$ with $f^{-1}(x)$: This gives us the inverse function. $f^{-1}(x) = \frac{x - 1}{2}$

So, the inverse function is $f^{-1}(x) = \frac{x - 1}{2}$.

Would you like more details, or do you have any other questions?

Here are some related questions:

1. How do you verify that two functions are inverses of each other?
2. What is the domain and range of the inverse function $f^{-1}(x) = \frac{x - 1}{2}$?
3. How does finding the inverse of a quadratic function differ from a linear function?
4. Can every function have an inverse? Why or why not?
5. How does the graph of a function compare to its inverse?

Tip: When finding the inverse function, always ensure that the original function is one-to-one, meaning it passes the Horizontal Line Test.