# 2017-05 Inequality for a continuous function

Suppose that $$f : (2, \infty) \to (-2, 2)$$ is a continuous function and there exists a positive constant $$m$$ such that $$| 1 + xf(x) + (f(x))^2 | \leq m$$ for any $$x > 2$$. Prove that, for any $$x > 2$$,
$\left| f(x) – \frac{\sqrt{x^2 -4}-x}{2} \right| \leq 6 \sqrt{m}.$

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