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

To find the inverse of the function f(x) = 2x + 1, we follow a systematic approach:

1. Replace f(x) with y:
   Start by rewriting the function as y = 2x + 1.
2. Swap the variables:
   To find the inverse, we switch x and y. This gives us:
3. x = 2y + 1
4. Solve for y:
   Now, we need to isolate y. Start by subtracting 1 from both sides:
5. x – 1 = 2y
6. Next, divide both sides by 2:
7. y = (x – 1) / 2
8. So, the inverse function:
   The inverse function is therefore:
9. f^-1(x) = (x – 1)/2

In summary, the inverse of the function f(x) = 2x + 1 is f^-1(x) = (x – 1)/2. This means that if you take an output from the original function and apply the inverse function, you will get back the original input.