A calculus problem by Ankit Nigam

Calculus Level 3

If y=\(f\left( x \right)\) be a real function so that \(3f\left( \frac { x+y }{ 3 } \right) =f\left( x \right) \quad +\quad f\left( y \right) \) for all x,y belongs to R and \(f\left( 0 \right)\) = 2 =\( f^{ ' }\left( 0 \right)\) , then the graph will be a

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