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Wiki

composition of an even function and an odd function is even

Is "composition order" significant here?

Let $f(x)$ - odd, $g(x)$ - even

It means only $f(g(x))$ is sure to be even?

Or both "$f(g(x))$ is sure to be even" and "$g(f(x))$ is sure to be even" ?

P.S. When a mathematician says "composition of F and G functions" - is it always 100% unambiguous? What is it? G(F(x)) ? First-mentioned function (F) is calculated first (so being "innermost")?

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    In theory, the order might matter to some authors and some readers. But you could just check and see whether it actually affects anything in this particular case. – Arthur Mar 31 '20 at 09:25
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    Even one even function in any number of compositions of even odd functions will make the overall composition even... – jeea Mar 31 '20 at 09:26
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    In either case, it's even.

    $EO(-x)=E(O(-x))=E(-O(x))=E(O(x))=EO(x)$

    $OE(-x)=O(E(-x))=O(E(x))=OE(x)$

     – Steven Alexis Gregory Mar 31 '20 at 09:33

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