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Continuous FE over reals, f(x)=(x+1)f(x^2) for x in R\{-1,1}

Source: SMMC 2024 B2

October 12, 2024

algebra

Problem Statement

Determine all continuous functions

f : \mathbb{R} \setminus \{1\} \to \mathbb{R}

that satisfy

f(x) = (x+1) f(x^2),

for all

x \in \mathbb{R} \setminus \{-1, 1\}