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An Odd Function (Posted on 2006-12-28) Difficulty: 3 of 5
Let f:R→R satisfy
  1. f(a)≠0 for some a in R
  2. f(xf(y))=yf(x) for all x,y in R
Prove that f(-x)=-f(x) for all x in R.

See The Solution Submitted by Bractals    
Rating: 3.8333 (6 votes)

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re: A final input | Comment 10 of 18 |
(In reply to A final input by Gamer)

Note that b does not take on all real numbers, just those where f(a)=ab for some a. Thus, for these b, f(b)=1/b.

It is also true that f(x)f(y)=f(xy); f(f(x)*f(y))=y*f(f(x)) which means f(f(x)*f(y))=xy, and f(x)f(y)=f(xy)


  Posted by Gamer on 2006-12-30 00:01:06
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