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March 9th, 2019, 06:22 AM   #1
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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.
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March 9th, 2019, 06:47 AM   #2
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Start by filling in some interesting values. For exampe x=0, y=1, ...
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March 9th, 2019, 07:22 AM   #3
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I’ve already tried.. the only thing that results is f(0)=0
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March 9th, 2019, 12:29 PM   #4
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f(2x)=2xf'(x). Interesting?
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