Why is the argument on the right? 
In most of Mathematics in English, the argument $x$ of a function (or partial map) $f$ with value $y$ is written $y=f(x)$ instead of, at least in Semigroup Theory and Formal Languages & Automata, $xf=y$. Why?

Thoughts:
A function $f$ is a subset of the Cartesian product of its domain $D$ and its codomain $C$ (i.e., $f\subseteq D\times C$) such that for each $d$ in $D$, $\lvert\{(d, c)\mid c\in C\}\rvert=1$. We write either $y=f(x)$ or $xf=y$ for $(x, y)\in f$.
The $xf=y$ notation has its strengths: composition of functions is usually taken left-to-right with this notation, as read in English, instead of right-to-left, with the argument $x$ first, as, I suppose, one usually has when evaluating $y$; one can read it as "$x$ through $f$ is $y$" instead of, say, "$y$ is $f$ at $x$"; and the left-to-right order respects that of going from the domain to the codomain.
Let me know if you can think of any strengths & weaknesses of the $xf=y$ notation.
I think history might have gotten the better of convention, that's all.
 A: Because before algebra, western mathematicians used prose, and presumably wrote things like "the sine of the angle." In making the transition from words to symbols, things were still read the same way, and it makes little sense to read $x\sin$ as "sine of $x$." The choice $\sin{x}$ is far more natural, and from there, $f(x).$ This example was relevant to Euler, to whom the choice is usually attributed.
Similar observations apply to, for example:


*

*the other trig functions,

*the exponential and logarithm functions,

*the notations $D$ and $\frac{\mathrm{d}}{\mathrm{d}x}$ for "the derivative (with respect to $x$) of" a function,

*$\operatorname{sgn}$ for "the sign of" a real number,

*$\operatorname{area}$ for "the area of" a plane region (or whatever).


Some slightly more modern, but still common, examples:


*

*$\operatorname{Pr}$ or $\operatorname{Prob}$ for "the probability of" an event

*$\mathcal{P}$ for "the power set of"

*$Z$ for "the number of zeroes of" a real- or complex-valued function

*$Z$ for the centre of a group (and other such things, like $N$ for the normalizer of a subgroup)

*$\operatorname{Gal}$ for "the Galois group of"


Doubtless, there are countless others; whenever people come up with a new function name, they're thinking "the such-and-such of...". The function notation is almost certainly also the inspiration for notations like ${GL}_{n}(R)$ and $T_{p}M$ for "the space tangent to $M$ at $p$", though I admit this last is a bit of a stretch unless you think of it slightly more abstractly as "the tangent space of...".
A: 
Hint:  According to A History of Mathematical Notations by F. Cajori this notation was  introduced by Johann Bernoulli  in  1718  . See this MSE post for a complete citation of the relevant section in the book.

