Composite functions
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Flip to reveal answersWhat does (f∘g)(x) mean?
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All 8 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 the outer function f.
Question
In f∘g, which function acts first?
Answer
g — the one written closest to x (read right-to-left).
Question
How do you build the formula for (f∘g)(x)?
Answer
Substitute the whole expression g(x) into f wherever f's input appears, then simplify.
Question
Is f∘g the same as g∘f?
Answer
Usually no — order matters, so they are generally different functions.
Question
f(x)=2x+1, g(x)=x−3. Find (f∘g)(5).
Answer
g(5)=2, then f(2)=2(2)+1=5.
Question
f(x)=x², g(x)=x+1. Find (f∘g)(x) and (g∘f)(x).
Answer
(f∘g)(x)=(x+1)²; (g∘f)(x)=x²+1. They differ.
Question
What two conditions give the domain of f(g(x))?
Answer
x must be allowed into g, AND g(x) must be a legal input for f.
Question
f(x)=√x, g(x)=x−4. Domain of (f∘g)(x)?
Answer
√(x−4) needs x−4 ≥ 0, so x ≥ 4.
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Full study notes for Composite functions
Topic 2.7 hub
Composite & inverse functions (HL only)
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