Is Function Composition Associative

MATHEMATICS · Subjective · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

54. Is Function Composition Associative? You already know that function composition is not commutative; that is, (f∘g)(x)≠(g∘f)(x)(f \circ g)(x) \neq(g \circ f)(x). But is function composition associative? That is, does (f∘(g∘h))(x)=((f∘g)∘h))(x)(f \circ(g \circ h))(x)=((f \circ g) \circ h)) (x) ? Explain your answer.

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