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November 16th, 2010, 09:51 AM  #1 
Newbie Joined: Nov 2010 Posts: 3 Thanks: 0  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? 
November 16th, 2010, 09:56 AM  #2 
Global Moderator Joined: Nov 2009 From: Northwest Arkansas Posts: 2,766 Thanks: 4  Re: Function Problem (please help)
0 if rational, 1 otherwise? No... Maybe Something similar 
November 16th, 2010, 09:59 AM  #3 
Newbie Joined: Nov 2010 Posts: 3 Thanks: 0  Re: Function Problem (please help)
I think the answer should be a formula..something like f(x)=x1...

November 16th, 2010, 10:18 AM  #4 
Global Moderator Joined: Nov 2009 From: Northwest Arkansas Posts: 2,766 Thanks: 4  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. 
November 16th, 2010, 10:30 AM  #5 
Newbie Joined: Nov 2010 Posts: 3 Thanks: 0  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 viceversa and i found it to be a constant too...but i found f(x)=1.

November 16th, 2010, 11:03 AM  #6 
Global Moderator Joined: Dec 2006 Posts: 19,291 Thanks: 1683 
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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