## siddhantsharan 3 years ago 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?

1. Ishaan94

f(x) = kx?

2. siddhantsharan

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

3. siddhantsharan

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

4. Ishaan94

f(x)=3x

5. Ishaan94

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

6. Ishaan94

Am I doing something wrong?

7. siddhantsharan

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.

8. Ishaan94

@KingGeorge

9. siddhantsharan

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

10. siddhantsharan

Thanks for Helping. :)