An algebra problem by Mateus Gomes

Algebra Level 4

For all real \( x \), define the function

\[ f(x) =\frac{1}{\sqrt[2011]{1-x^{2011}}}\]

Calculate \( {(f(f(f(\ldots(f(2011))\ldots)))}^{2011}\), where \(f\) is applied 2010 times.

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