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.

{2010}^{2011}

{2011}^{2010}

{2011}^{2012}

{2011}^{2011}

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