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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](http://meta.math.stackexchange.com/questions/5020/), [here](http://meta.stackexchange.com/a/70559/155238), [here](http://meta.math.stackexchange.com/questions/1773/) and [here](http://math.stackexchange.com/editing-help#latex).2012-11-10

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