2013-13 Functional equation

Find all continuous functions \(f : \mathbb{R} \to \mathbb{R}\) satisfying
\[
f(x) = f(x^2 + \frac{x}{3} + \frac{1}{9} )
\]
for all \( x \in \mathbb{R} \).

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2013-13 Functional equation , 4.3 out of 5 based on 37 ratings