Is the composing of functions always commutative?

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I have a question for my math study. It seems quite simple, but I just can't find a counterexample for the following:

The composition of two functions is always commutative

Could you help me with that?

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2 Answers

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Simple. Take $f(x) = x^3, g(x) = 2x$. Then $f(g(x)) = (2x)^3 = 8x^3$, while $g(f(x)) = 2x^3$.

No thanks

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just check out matrix multiplication which is almost never commutative. But of course there are examples where the matrix multiplication is commutative so this a good source for both cases.

bests

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