# Is there such a thing as function decomposability?

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

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For some basic information about writing math at this site see e.g. here, here, here and here. –  Julian Kuelshammer Nov 10 '12 at 10:33
I don't know of any standard terminology for this property. I think "decomposability" is a fine term when defined in context. An interesting example of such a function is $f(f(x)) = x^2+1$.