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?

Answer 1

f(x) = kx?

Answer 2

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

Answer 3

Oh i missed some info.

**
f(0) = 0 , f'(0) = 3

Answer 4

f(x)=3x

Answer 5

How is the function f(x)=kx not differentiable on/in R. Hmm

\[\lim_{h \to 0} \frac{3(x+h) - 3x}{h}\]

Answer 6

Am I doing something wrong?

Answer 7

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.

Answer 8

@KingGeorge

Answer 9

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

Answer 10

Thanks for Helping. :)