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Flip to reveal answersWhat does (f∘g)(x) mean?
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All 9 Flashcards — Composite functions
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Question
What does (f∘g)(x) mean?
Answer
f(g(x)) — apply the inner function g first, then f. Read right-to-left.
Question
Does f∘g equal g∘f?
Answer
Not in general — order matters; the inner function changes the result.
Question
How do you evaluate (f∘g)(a) at a number?
Answer
Compute g(a) first, then put that value into f. Work inside-out.
Question
How do you form the composite expression (f∘g)(x)?
Answer
Replace every x in f with the whole expression g(x) (in brackets), then simplify.
Question
f(x) = 2x + 1, g(x) = x². Find (f∘g)(x).
Answer
f(x²) = 2x² + 1.
Question
f(x) = 2x + 1, g(x) = x². Find (g∘f)(x).
Answer
g(2x + 1) = (2x + 1)² = 4x² + 4x + 1.
Question
How do you solve a composite equation like (f∘g)(x) = k?
Answer
Form the composite expression, set it equal to k, and solve for x.
Question
How do you find f given g and (f∘g)(x)?
Answer
Compose with the unknown f, then match coefficients to the given result.
Question
Common composite mistake?
Answer
Doing the functions in the wrong order, or forgetting brackets when substituting (e.g. (2x+1)²).
Read the notes
Full study notes for Composite functions
Topic 2.5 hub
Composite & inverse functions
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Math AA SL exam skills
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