[thaumasiotes]

> See e.g. Page 2 and the following example of https://billcookmath.com/courses/math4010-spring2016/math401... (2016)

There appears to be a typo in that example; I assume "Essentially elementary functions are the functions that can be built from ℂ and f(x) = x" should say something more like "the functions that can be built from ℂ and f(x) = y".

[reikonomusha]

Not a typo! Think of f(x) = x as a seed function that can be used to build other functions. It's one way to avoid talking about "variables" as a "data type" and just keep everything about functions. We can make a function like x + x*exp(log(x)) by "formally" writing

    f + f*(exp∘log)

where + and * are understood to produce new functions. Sort of Haskell-y.