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.
by
Akshat Sharda