# 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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