Why does no one use the notation $f(x)^2$?

It seems to me that "$f(x)^2$" couldn't mean anything other than "$[f(x)]^2$", so there shouldn't be any ambiguity involved, but people always tend to put an extra pair of brackets around the "$f(x)$" everywhere I see it squared. Is there a reason for this?

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Perhaps because some people think $f (x)^2$ could mean $f (x^2)$. This is reasonable when $x$ is some big complicated expression like $\sum \frac{x^n}{n!}$... –  Zhen Lin Mar 26 '12 at 2:30
Isn't the usual notation "$f^2(x)$?" –  ThisIsNotAnId Mar 26 '12 at 3:10
I think $f(x)^2$ just looks quite ugly (maybe because I don't immediately see what's being squared exactly at a glance)... That's certainly the reason why I prefer extra brackets. –  Sam Mar 26 '12 at 3:30
@Sam But it's not ugly for a programmer. ;) For me it's definitely $f(x)\,f(x)$ –  Calmarius Jun 30 '13 at 7:40

The primary concern is that the parenthesized quantity will be viewed as squared, rather than the function. There can be ambiguity when you're unsure of whether the person is being sloppy by considering the argument as squared and just leaving off the brackets around $(x)^2$.