Let $ f : \mathbb R ^ + \to \mathbb R $ be an increasing function such that $ x f ( x ) + 2 > 0 $ and $ f ( x ) f \left( \frac { x f ( x ) + 4 } x \right) = 1 $. Find $ f ( x ) $.
I tried to solve it by replacing $ x $ with $ \frac 4 x $, but didn't get anything. I also tried to make a quadratic by assuming $ f ( x ) = t $ and then finding $ t $ but this didn't go anywhere either. Any help would be appreciated.