Why do we apply functions the "wrong way around", i.e. why do we write $f(x)$ instead of $(x)f$?

The origin of $f(x)$ in Euler 1734, and Euler's frequent use of $fx$ (which he learned from his teacher, Johann Bernoulli) and $f:x$, have been discussed here before. I'm not sure of their motives (although my guess would be $f$ of $x$ is a more natural choice for pronunciation than $x$'s $f$), but they were prolific enough to be among the most influential mathematicians when it comes to notational conventions.

Because after all, all we have is a notational convention. As if to make things more confusing, some operations are represented to the right, e.g $x$ squared is $x^2$ rather than, say, $\operatorname{sq}x$ or $\operatorname{pow}_2 x$.