Two Radicals on a Square

★ 8/10functions algebra Cauchy-Schwarz inequality Casework

Problem

For $x, y \in [0, 1]$ , find the range of

f(x, y) = \sqrt{\frac{1 + xy}{1 + x^2}} + \sqrt{\frac{1 - xy}{1 + y^2}}.

Answer

Solution

Difficulty	8/10
Topics	functions, algebra, Cauchy-Schwarz, inequality, Casework

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