# 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.

×