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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)

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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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