Fractional Function

Algebra Level 4

Let ff be a function defined as f(x+y2)=f(x)+f(y)2f\left(\dfrac{x+y}{2}\right)=\dfrac{f(x)+f(y)}{2} for any real numbers xx and y.y. If f(0)=1f'(0)=-1 and f(0)=1,f(0)=1 , what is the value of f(2)?f(2)?

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