A Two-Variable Functional Inequality

★ 8/10functions Completing the Square inequality Functional Equations

Problem

Let $a, b > 0$ and $f(x) = ax^2 + b$ . Suppose

f(xy) + f(x + y) \geqslant f(x)f(y) \qquad \text{for all } x, y \in \mathbb{R}.

Find all conditions on $a$ and $b$ for this to hold.

Answer

Solution

Difficulty	8/10
Topics	functions, Completing the Square, inequality, Functional Equations

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