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As far as I understand we write $\cos^2 x$ just to not mix up $(\cos x)^2$ with $\cos(x^2)$. But it is difficult to associate $f(x)^2$ with anything else but $(f(x))^2$. Is it correct to use such a notation?

faleichik
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    Use as $\cos^{2}\left(x\right)$. Use $\large\tt always$ $\left(~~\right)$ in a function call. In this place, that is always an obvious mistake. – Felix Marin Jan 07 '14 at 22:24
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    Opionions on notation differ (and some people have very strong opinions about certains points of notation). For what it's worth, I personally consider $f(x)^2$ correct. – fkraiem Jan 07 '14 at 22:25
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    It's unambiguous and it's even preferable to $f^2(x)$ which could mean $f(f(x))$ (If $f:X\to X$ of course). – Stefan Hamcke Jan 07 '14 at 22:26
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    I agree, it is OK to write $f(x)^2$, meaning $(f(x))^2$. But don't go so far as to claim those using other notation are wrong. – GEdgar Jan 07 '14 at 22:36
  • @faleichik : Yes, it is. – Stefan Smith Jan 08 '14 at 01:57

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by convention $$\cos^2x=(\cos x)^2$$ if $$f^2(x)=f(f(x))$$ then must be $$\cos^2x=\cos(\cos x)$$ in general $$(\cos x)^2\neq\cos(\cos x)$$ Evidently using such notation is not correct but we use.

Adi Dani
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