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 January 10th, 2011, 10:53 AM #1 Newbie   Joined: Sep 2009 Posts: 28 Thanks: 0 Finding a real function Hi, Can we find a function $f:\mathbb{R} \rightarrow \mathbb{R}$ verifying : $f(x)-f(y)=\sqrt {x^2+y^2}$ ? Thanks a lot
 January 10th, 2011, 11:16 AM #2 Newbie   Joined: Dec 2010 Posts: 18 Thanks: 0 Re: Finding a real function No, take x=y. Left hand side has to be 0, right hand side almost never will be.
January 10th, 2011, 11:24 AM   #3
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Re: Finding a real function

Quote:
 Originally Posted by Thommy No, take x=y. Left hand side has to be 0, right hand side almost never will be.
I think in this case the relation stands, isn't it ?

January 10th, 2011, 11:38 AM   #4
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Re: Finding a real function

Quote:
Originally Posted by rmas
Quote:
 Originally Posted by Thommy No, take x=y. Left hand side has to be 0, right hand side almost never will be.
I think in this case the relation stands, isn't it ?
You need something that will work for all x and y, not just some.

January 10th, 2011, 11:47 AM   #5
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Re: Finding a real function

Quote:
Originally Posted by CRGreathouse
Quote:
Originally Posted by rmas
Quote:
 Originally Posted by Thommy No, take x=y. Left hand side has to be 0, right hand side almost never will be.
I think in this case the relation stands, isn't it ?
You need something that will work for all x and y, not just some.
What about the cases where x,y are not 0 and x != y ?

January 10th, 2011, 01:36 PM   #6
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Re: Finding a real function

Quote:
 Originally Posted by rmas What about the cases where x,y are not 0 and x != y ?

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