To find the inverse of the function f(x) = 2x + 1, we will follow a series of steps.
1. Start by replacing f(x) with y:
y = 2x + 1
2. Next, we need to solve for x in terms of y. First, we can subtract 1 from both sides:
y – 1 = 2x
3. Now, divide both sides by 2:
x = (y – 1) / 2
4. Finally, to express the inverse function, we will interchange x and y. Therefore, we write:
f-1(x) = (x – 1) / 2
So, the inverse of the function f(x) = 2x + 1 is f-1(x) = (x – 1) / 2.