MathDB

FE with continuity

Source: Romanian District Olympiad 2023 11.1

March 11, 2023

functional equationcontinuityalgebra

Problem Statement

Determine all continuous functions

f:\mathbb{R}\to\mathbb{R}

for which

f(1)=e

and

f(x+y)=e^{3xy}\cdot f(x)f(y),

for all real numbers

x{}

and

y{}

.

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