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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(2): A final input | Comment 9 of 18 |
(In reply to re: A final input by JLo)

 
Does the following function satisfy the
restrictions of the problem?
  f(x) = (-1)^p*2^r*3^q 
         if x = (-1)^p*2^q*3^r for p in {0,1} and q,r in Z
       = x
         otherwise 
If not, can you show me where it fails.
 

  Posted by Bractals on 2006-12-29 23:52:02
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