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An Odd Function (Posted on 2006-12-28)

Let f:R→R satisfy

f(a)≠0 for some a in R
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.)

thanx Gamer

| Comment 17 of 18 |

We only substitute x=0 and y=0, but that does not mean that variable y is dependent on variable x, right ? or it doesn't matter, I just want to be sure.

Thanks again

Posted by Ferdinand on 2006-12-30 19:49:46

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