Functional Integrations

Calculus Level 3

Let \(f : \mathbb {R \to R} \) be a continuous function such that \(f(x) = f(2x)\) is true \(\forall \ x \in \mathbb R\) and \(f(1)=3\). Find \(\displaystyle \int_{-1}^1 f(f(f(x))) \, dx \).

\[\] Notation: \(\mathbb R \) denotes the set of real numbers.

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