"Composition of an even and an odd function is even" means both $f(g(x))$ and "$g(f(x))$ are even?

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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")?