Why do we put the f on the left of x?

Question

Does anyone know how historically we came to notate functions as f(x) instead of (x)f? For example g(f(x)) instead of ((x)f)g or for matrices B A x instead of x A B.

After all (in the Western world) we write from left to right, but in mathematics we notate operations from right to left. Also if anyone of Arabian origin sees that, does it mean you don't have that particular confusion?

Answer 1

This is consistent with English syntax and with the concept of "function" being a special kind of relation on sets.

Look at the relationship "Husband of": In English this is typically expressed, for example, as Husband of Hillary Clinton is Bill Clinton.

In mathematical notation this gets naturally translated maintaining the syntax order: H(Hillary) = Bill

Successor of Obama is Trump (in US presidency)

$S(n) = n+1$ (Successor function in natural numbers)

Answer 2

There are times when $f(x)$ is written $xf$. It's merely a case of trying to use the accepted convention except when it is inconvenient to do so; in which case you state that you are doing it differently and then proceed to do so.

Answer 3

To my recollection this notation goes back to Leonard Euler.