VJIMC 2017, Category I, Problem 1 : Functional Equation

by adityaguharoy, Apr 6, 2017, 3:59 AM

Problem : (The problem that appeared after translation )
Let $f:\mathbb{R} \to \mathbb{R}$ be a continuous function satisfying
\[f(x+2y)=2f(x)f(y)\]for every $x,y \in \mathbb{R}$. Prove that $f$ is constant.

Solution
VJIMC
functional equation
algebra
Category I

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