My Math Forum Need help with a functional equation

 Algebra Pre-Algebra and Basic Algebra Math Forum

 March 9th, 2019, 06:22 AM #1 Newbie   Joined: Mar 2019 From: USA Posts: 4 Thanks: 0 Need help with a functional equation $$f: \mathbb{R} \to \mathbb{R}\qquad \frac{f(x+y)}{x+y} = \frac{f(x)-f(y)}{x-y}, \qquad \forall x,y\in \mathbb{R}, \left|x\right| \neq \left|y\right|$$ 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: 752 Thanks: 261 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: 6,704 Thanks: 670 f(2x)=2xf'(x). Interesting?

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