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Inverse functions

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Useful for: MCR3U IB Math AA SL & HL IB Math AI SL & HL AP® Precalculus

Learn it The inverse f⁻¹ undoes f: swap x and y, then solve for y. Its graph is the reflection of f in the line y = x, and the domain and range swap. A function only has an inverse function if it is one-to-one (you may need to restrict the domain).

Example: Find the inverse of f(x) = (2x − 5)/3.

  1. y = (2x − 5)/3. Swap: x = (2y − 5)/3.
  2. 3x = 2y − 5 → y = (3x + 5)/2.
  3. f⁻¹(x) = (3x + 5)/2.

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