To find the inverse function of f(x) = 2x + 3, we need to follow a few systematic steps.
- Start by replacing f(x) with y:
We rewrite the function asy = 2x + 3
. - Swap x and y:
This gives usx = 2y + 3
. - Solve for y:
We need to isolate y on one side of the equation. Start by subtracting 3 from both sides:
x - 3 = 2y
.Next, divide both sides by 2 to solve for y:
y = (x - 3) / 2
. - Replace y with f-1(x):
This gives us the inverse function, which isf-1(x) = (x - 3) / 2
.
Therefore, the inverse of the function f(x) = 2x + 3 is f-1(x) = (x – 3) / 2. This inverse function effectively undoes the operations of the original function.