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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: explanation of expression (1) | Comment 16 of 18 |
(In reply to problem with expression (1) by Ferdinand)

Substituting x=0 and y=0 gives f(0*f(0))=0*f(0) by condition 2.

We don't know what f(0) is yet, but it's clear that anything it could be times 0 must be 0. So it reduces to f(0)=0.

  Posted by Gamer on 2006-12-30 18:55:12
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