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$f(x)^2$ 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?

Jochem Kuijpers
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    It is worth pointing out that $f^2$ is somewhat ambiguous whether we are talking about $f\cdot f$ or if we are talking about $f\circ f$, just as $f^{-1}$ is ambiguous whether we are talking about the multiplicative inverse of $f$ or the functional inverse of $f$. Better to avoid it in my opinion. – JMoravitz Oct 13 '19 at 01:42
  • Also related: https://math.stackexchange.com/questions/208363/conventions-for-notation-of-function-exponentation?noredirect=1&lq=1 – JMoravitz Oct 13 '19 at 01:50

1 Answers1

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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.

cmk
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