Math archive (10)

Calculus Level 4

If \(f:\mathbb R^{+}\rightarrow\mathbb R\) and \(f(x)f(y)=f(xy)+2\left(\frac{x+y}{xy}+1\right)\) for all positive \(x,y\). Find \(3\) times the sum of all possible values of \(f\left(\frac{1}{2}\right)\).

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