Double Symmetry

★ 6/10functions Functional Equations Symmetry

Problem

A function $f(x)$ is defined on $\mathbb{R}$ , $f(x+1)$ is odd, $f(x+2)$ is even, and for $x \in [1, 2]$ , $f(x) = ax^2 + b$ . If $f(0) + f(3) = 6$ , find $f\!\left(\dfrac{9}{2}\right)$ .

Answer

Solution

Difficulty	6/10
Topics	functions, Functional Equations, Symmetry

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