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Composite functions f(g(x))

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

Learn it f(g(x)), also written (f ∘ g)(x), means: first apply g, then apply f to the result. Work from the inside out. In general f(g(x)) ≠ g(f(x)).

Example: f(x) = 2x + 1 and g(x) = x². Find f(g(3)) and g(f(x)).

  1. g(3) = 9, so f(g(3)) = f(9) = 19.
  2. g(f(x)) = (2x + 1)² = 4x² + 4x + 1.

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