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?

Question

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?

anonymous · Answer

f(x) = kx?

anonymous · Answer

I know. 
It seems like that.
But apparently not. 
As in the answer it's NOT differenciable in R.

anonymous · Answer

Oh i missed some info.

** 
f(0) = 0 , f'(0) = 3

anonymous · Answer

f(x)=3x

anonymous · Answer

How is the function f(x)=kx not differentiable on/in R.  Hmm

$$\lim_{h \to 0} \frac{3(x+h) - 3x}{h}$$

anonymous · Answer

Am I doing something wrong?

anonymous · Answer

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.

anonymous · Answer

@KingGeorge

anonymous · Answer

Oh well. I guess the answer may be wrong then.
All of us cant go wrong.

anonymous · Answer

Thanks for Helping. :)