TITLE: What is the property where f(g(x)) = g(f(x))?
QUESTION [9 upvotes]: What is the property where f(g(x)) = g(f(x))?

REPLY [15 votes]: 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.