# 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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