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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)

Comments: ( Back to comment list | You must be logged in to post comments.)
re(3): A final input | Comment 13 of 18 |
(In reply to re(2): A final input by Bractals)

I realized I made a mistake by assuming f(x^r)=f(x)^r for all real numbers r at some point, although I have proven it only for rational r. Maybe there are more than two solutions after all... I still think they'd have to be discontinuous everywhere.
  Posted by JLo on 2006-12-30 06:58:23

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