# Functions and Behudapanti

Algebra Level 4

A non-zero polynomial $$f$$ satisfies

$f(f(x)) = (x + x^2 + x^3 + \ldots) f(f(f(x))$

for all $$0 < x < 1$$. Determine the smallest value of $$f(x)^2 + x$$ where $$x$$ ranges over all real numbers.

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