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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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x and y are independent Comment 18 of 18 |
(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.

  Posted by Gamer on 2006-12-31 01:49:07

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