What is the inverse of the function f(x) = 2x + 1?

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

1. Replace f(x) with y:

   We start by rewriting the function as:

   y = 2x + 1

2. Swap x and y:

   Next, we exchange the variables x and y:

   x = 2y + 1

3. Solve for y:

   Now, we need to isolate y:

   x - 1 = 2y
   
   y = (x - 1) / 2

4. Write the inverse function:

   Now that we have y isolated, we can express the inverse function:

   f^-1(x) = (x – 1) / 2

In conclusion, the inverse of the function f(x) = 2x + 1 is f^-1(x) = (x – 1) / 2. This means that when we input a value into the inverse function, we should get back the original value that was used in the function f(x).