Let f:R to R be a function such that f((...

Let `f:R to R` be a function such that `f((x+y)/(3))=(f(x)+f(y))/(3)"for all "x,y in R`
f(0)=0 and f'(0)=3. Then, f(x) is

A

`(f(x))/(x^(2))` is differentiable in R

B

`f(x)` is continuous but not differentiable in R

C

f(x) is continuous in R

D

f(x) is bounded in R

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The correct Answer is:

C

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