Notation of a function raised to a power

Question

$f(x)^2$ is sometimes written as $f^2(x)$.

Why is it not written as $f(x)^2$?

Is it just a matter of taste or convention?

Answer 1

It's probably because the notation could make it clear that the function is $f^2=f\cdot f$. That is, if $g=f^2=f\cdot f,$ then we'd write $g(x)=f^2(x).$ Writing $f(x)^2$ kind of hides the functional relationship. Although, as noted in the comments, writing $f^2(x)$ could be confused with composition. It's probably best to clarify what you mean when you write it. You could also write $(f(x))^2,$ which has a pretty clear meaning.