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Let f:R->R be a function such that f((...

Let `f:R->R` be a function such that `f((x+y)/3)=(f(x)+f(y))/3 ,f(0) = 0 and f'(0)=3` ,then

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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