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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