I am not a mathematician, so what I ask might be trivial, however I couldn't find something relevant in the web. My question is the following:
Is there a formal notation for functions that comply the following
$$f(x_1, ..., x_n) = g(f(x_1), ..., g(f(x_n))$$
and if there is such a property, how is it called? The current, intuitive name I can think of is decomposable functions, but I don't know if formally there is such a thing.
Example 1: An additive function would be decomposable.
Example 2: A multiplicative function would also be decomposable