Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I read a previous question here but it seems incomplete for me (missing references).

Given a generic function, $ f $ :
1. is true that $ f^2 $ means $ f^2(x) = (f \circ f)(x) = f(f(x)) $ ?
2. or is true that $ f^2 $ means $ f^2(x) = (f(x))^2 $ ?

With your answers can you write also some references?
Anyway if (2) holds, then is $ (f \circ f)(x) $ the only way to write $ f(f(x)) $ ?
Instead, if (1) holds, then why do some books write $ \ln^2(x) = (\ln(x))^2 $ or the trigonometric identity $ \sin^2(x)+\cos^2(x) = 1 $ ?

Thanks for answers.

share|improve this question
1  
It is often used in both ways (just not in the same context). You'll simply have to determine which is intended from the situation. –  Cameron Buie Oct 6 '12 at 20:23
2  
I'ld also suggest you to read the answer given here math.stackexchange.com/questions/30317/arcsin-written-as-sin-1x as it is quite well written –  TheJoker Oct 6 '12 at 20:26
2  
If you want an opinion on that, here is mine: Use $f^n(x) := (f(x))^n$ only if $f$ is a standard function. It is very common for trigonometric and hyperbolical functions, but that's about it. –  filmor Oct 6 '12 at 20:28
    
thanks for answers. Filmor brought a good argument (even if i'm a Gauss fan here xD ) and now i'm reading the link about arcsin. –  Pierfrancesco PierQR Aiello Oct 7 '12 at 6:32

1 Answer 1

up vote 0 down vote accepted

I've seen both. I seem to recall having read somewhere (Therefore it's true! Right?) that Gauss objected to writing $\sin^2 x$ for $(\sin x)^2$ on the grounds that $\sin^2x$ ought to mean $\sin\sin x$. I'm inclined to agree with Gauss, but then there's King Canute and all that.

Certainly using $f^2$ to mean $f\circ f$ is consistent with the usual notation by which $f^{-1}$ means the inverse function.

share|improve this answer
    
I inclined to agree with Gauss too :P –  Pierfrancesco PierQR Aiello Oct 7 '12 at 6:10

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.