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Missing something. Functions. Let f : R -> R be a function such that : f( (x+y) /3) = [f(x) + f(y)] /3 then: Is f(x) differentiable in R? Is it continous? Is f(x)/x differentiable?

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f(x) = kx?
I know. It seems like that. But apparently not. As in the answer it's NOT differenciable in R.
Oh i missed some info. ** f(0) = 0 , f'(0) = 3

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Other answers:

How is the function f(x)=kx not differentiable on/in R. Hmm \[\lim_{h \to 0} \frac{3(x+h) - 3x}{h}\]
Am I doing something wrong?
Did you differenciate-Put x=0---integrate? { To get the function} Or observe? :P-- That works here too . I got the same thing too. I dunno whats wrong.
Oh well. I guess the answer may be wrong then. All of us cant go wrong.
Thanks for Helping. :)

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