Fun(ctional) equation #2

Algebra Level 4

\[2f(x)=f(xy)+f\left(\dfrac{x}{y}\right)\]

If the above equation is true for all \(x,y\in \mathbb{R}^{+}\) and \(f(1)=0, f'(1)=1\), then find the closed form of \( f(1000)\) to 3 decimal places.

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