Let f:R→R satisfy
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f(a)≠0 for some a in R
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f(xf(y))=yf(x) for all x,y in R
Prove that f(-x)=-f(x) for all x in R.
(In reply to
y is independent by Gamer)
In this case, think of equation 2 as being dependent on two variables. What makes this function interesting, is no matter what two real numbers you choose for x and y, that equation holds true. (You can choose whatever real x and y you want.)
The proof that f(0)=0 doesn't imply that x=y always, but it does for that part.
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Posted by Gamer
on 2006-12-31 01:49:07 |
x and y are independent
