‘Correct’ way of writing a function?

Question

So for all these years, I have been writing a function f(x) as $\mathop{f}(x)$.

But now that I begin to think about a correct way of writing a function, what should it be?

Is it f(x) or \mathop{f}(x) or \mathop{f}\left(x\right) or f\left(x\right)?

Or is it actually none of these?

Answer 1

I simply use f(x) (inside a formula, that is, between $...$ or \[...\] or any other mathematical construct, which shall be implicit in what follows) and consider all the other proposed usages wrong. One might argue about \mathop{\kern0pt f}(x) so a thin space would be added in front of the f if preceded by certain kinds of atoms (what happens for \sin and \log). A definition should be

\newcommand{\fn}[1]{\mathop{\kern0pt #1}\nolimits}

and \fn{f}(x) would give the desired result.

However, the following example shows that it is suboptimal: there is no reason for the thin space.

\documentclass{article}

\newcommand{\fn}[1]{\mathop{\kern0pt #1}\nolimits}

\begin{document}

$g(x)f(x)$

$\fn{g}(x)\fn{f}(x)$

$f(x)\ne f'(x)$

$\fn{f}(x)\ne \fn{f}'(x)$

\end{document}

Answer 2

If your typoscript is to be processed (not retyped) by a scientific journal or book publisher, then stick to conventions and keep it as simple as possible lest you will annoy the copy editor. Hence f(x). Or f\left(\frac{a}{b}\right) if the function argument has extra height or depth.

If you are your own editor, then, as others have said, there is no such category as "correctness". Still: why not keep things simple?