What are the functions that make composite functions called?

Question

What do you call the functions that make a composite function.

Example : $e^{\sin x} $ is made up of $\sin x$ in the argument of $e^x$

So what are $\sin x$ and $e^x$ called here in this context? Basic functions or something?

(Please don't tell me the former is trig and latter is exponential function, I know that, but that's not what I'm asking here, please try to understand)

Hope I made myself clear.

Answer 1

I'm not sure I understood your question correctly, but maybe the term you want is elementary function?

Or if, as Thomas Andrews suggested, what you want is analogous to the term "factors" for the factors $a,b,c$ in a product $a\cdot b\cdot c$, I think the word you want is "component". The components in your expression have been composed into a larger express, so "component"is just right.

In some contexts, combinatory logic in particular, the function $g(x)$ in $f(g(x))$ is commonly called the applicand of $f$, but the context you're asking about is so far removed from this that "applicand" might just confuse people. Or maybe not! But if there's a corresponding term for the $f$ part of $f(g(x))$ I can't think what it is.

Answer 2

To short circuit the comments back and forth I'll provide a (community wiki) answer.

I know of no established terminology for this. If you need one for something you are writing I think "components" would be appropriate. The "compo" prefix nicely suggests "composition". Be sure to define that term for your readers, and note that the order in which you compose matters.

-- Ethan Bolker

You could also (if you were writing an article discussing this extensively, and had to use the words over and over) invent your own words, in analogy with "summand" or "multiplicand"; because of the asymmetry of the relation, I'd aim for an analogy with division or subtraction: you might, for instance, call the outer function the "composer" and the inner the "composand". Words like this are not (as far as I know) in common use, perhaps because the need for them hasn't arisen as often as those for the elementary arithmetic operations.

-- John Hughes