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March 9th, 2019, 06:22 AM  #1 
Newbie Joined: Mar 2019 From: USA Posts: 4 Thanks: 0  Need help with a functional equation
$$ f: \mathbb{R} \to \mathbb{R}\qquad \frac{f(x+y)}{x+y} = \frac{f(x)f(y)}{xy}, \qquad \forall x,y\in \mathbb{R}, \leftx\right \neq \lefty\right $$ Can I prove anything interesting about this function? I need to find it. 
March 9th, 2019, 06:47 AM  #2 
Senior Member Joined: Oct 2009 Posts: 798 Thanks: 298 
Start by filling in some interesting values. For exampe x=0, y=1, ...

March 9th, 2019, 07:22 AM  #3 
Newbie Joined: Mar 2019 From: USA Posts: 4 Thanks: 0 
I’ve already tried.. the only thing that results is f(0)=0

March 9th, 2019, 12:29 PM  #4 
Global Moderator Joined: May 2007 Posts: 6,768 Thanks: 699 
f(2x)=2xf'(x). Interesting?


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ecuation, equation, functional 
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