Precalculus

How to solve

An inverse undoes a function: if f sends x to y, f⁻¹ sends y back to x. For a linear map, swap input and output and solve for the new output — that algebraic swap encodes the undo steps in reverse order.

Steps

  1. Replace f(x) with y.
  2. Swap x and y, then solve for y.
  3. Rename y as f⁻¹(x).

Example

Find the inverse of f(x) = 2x + 3.

  1. y = 2x + 3; swap: x = 2y + 3.
  2. x − 3 = 2y ⇒ y = (x − 3)/2.
  3. f⁻¹(x) = (x − 3)/2.

Answer: (x-3)/2

How to type answers

  • Enter like (x-3)/2 or x/2-3/2
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