MP111
Problem for February 2012 

Does there exist a bounded real-valued function $f(x)$ with $f(1) > 0$ such that for all real numbers $x$ and $y$,
$$\left(f(x+y)\right)^2 \ge \left(f(x)\right)^2 + 2f(xy) +\left(f(y)\right)^2 .$$

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