Can the functions that have only $1$ variable in their argument be called a composite function?

Question

Can I call functions like $\sin x , \tan^{-1} x , e^ x $ etc composite functions too?

If not, then what do I call them? I mean taking individual names like exponential function, sine function etc doesn't seem convenient. What is correct term for this? How do I refer to these functions?

To be more specific. Eg : the natural numbers greater than 1 that are not prime are called composite numbers. And those that are not composite are prime numbers. It either prime or composite.

So how do I refer to functions that are not composite functions? Do we have a word for them? Like Prime function or something?

Answer 1

Some functions are obviously composite, such as $$f(x)=e^{\sin x}$$ or $$f(x)= \tan^ {-1} (x^2+1)$$

Other functions can be considered as composite functions.

For example the identity function $id(x)=x$ could be considered as$$ id(x)=fof^{-1}(x)$$ for any bijective function $f(x).$

Answer 2

A function $f:\>A\to B$ is a function, namely a subset $f\subset A\times B$ satisfying certain conditions.

If a function $f:\>A\to B$ is given, and you can find a set $C$, together with functions $g:\>A\to C$ and $h:\>C\to B$ such that $f=h\circ g$ (where $\circ$ is properly defined) then $f$ is called the composition of $g$ with $h$.

Of course you can collect a list of functions occurring in calculus 101, like $$x\mapsto x,\quad x\mapsto x^2,\quad \exp,\quad\log,\quad\sin,\quad x\mapsto\sqrt{x},\quad{\rm etc.}\ ,$$ and call them basic functions of calculus, but the members of this list are up to personal taste. In any case, there is no such thing as a prime function with respect to composition.