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Let $f$ and $g$ be two functions, both of them from $\Bbb R$ to $\Bbb R$, defined by the formulas:

$ f: x \mapsto x\sqrt{x^2+4} $ and

$g: x \mapsto x^3 + 3x \\ $

I saw, in an exercise, that $f \circ g = g \circ f$, but even if I can compute it, I can’t understand, why do they commute?

Nij
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Jérémie Delage
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  • "even if I can compute it, I can't understand why they do commute." Well... can you compute it? Have you checked via computation that they actually do commute? Can you show us your working? – Adam Rubinson Apr 16 '22 at 21:05
  • There is no real understanding why as far as I can see from the above. Perhaps there is a complex perspective that elaborates? – copper.hat Apr 16 '22 at 21:20
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    I don't understand what's bothering you. Are you asking for a proof that the two maps commute? Are you asking how you could guess, at first sight, if two maps commute? – Plop Apr 16 '22 at 21:21
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    Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking. – Community Apr 16 '22 at 21:21

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