What is the property where f(g(x)) = g(f(x))?
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Besides being called (composition) commutative, it is sometimes also said that such functions are permutable, e.g. see here. As an example, a classic result of Ritt shows that permutable polynomials are, up to a linear homeomorphism, either both powers of x, both iterates of the same polynomial, or both Chebychev polynomials.
We say $f$ and $g$ commute (with respect to composition). The property is called "commutativity".
"Associativity" is the property that says that $f\circ (g\circ h)$ is the same as $(f\circ g)\circ h$, where $\circ$ is composition.