What is the inverse function of f(x) = 2x + 3?

To find the inverse function of f(x) = 2x + 3, we need to follow a few systematic steps.

  1. Start by replacing f(x) with y:
    We rewrite the function as y = 2x + 3.
  2. Swap x and y:
    This gives us x = 2y + 3.
  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.

  4. Replace y with f-1(x):
    This gives us the inverse function, which is f-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.

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