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November 16th, 2010, 09:51 AM   #1
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Function Problem (please help)

Determine the function f:R->R , f(0)<>0, f(x)*f(y)=f(y+xy) for any x,y from R.
Any ideas?
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November 16th, 2010, 09:56 AM   #2
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Re: Function Problem (please help)

0 if rational, 1 otherwise? No... Maybe
Something similar
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November 16th, 2010, 09:59 AM   #3
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Re: Function Problem (please help)

I think the answer should be a formula..something like f(x)=x-1...
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November 16th, 2010, 10:18 AM   #4
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Re: Function Problem (please help)

Ok. I'm looking for something besides f(x) ? 0. When you say "determine the function...", I get the implication that there is only one.
A few trial and error computations have led me to believe that (almost?) all of the function values are the same constant, so zero would certainly satisfy that.
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November 16th, 2010, 10:30 AM   #5
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Re: Function Problem (please help)

Yes...there should be only one...I also tried some particular cases such as x=1 and y=0 and vice-versa and i found it to be a constant too...but i found f(x)=1.
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November 16th, 2010, 11:03 AM   #6
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For any x, putting y = 0 gives f(x)*f(0) = f(0), then dividing by f(0) gives f(x) = 1. As this problem is trivial, was it stated correctly?
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