Fractional Function

Algebra Level 4

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

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