# Evaluating a Complex Function

Algebra Level 4

Consider the function $$f(x)=\frac {1} {\sqrt {1-x^2} }$$ which is defined for all complex numbers apart from 1 and -1. $$f^{(2011)} ( \frac {1} {5} )$$ has the form $$\frac {a\sqrt{b}} {c}$$, where $$a$$ and $$c$$ are coprime integers and $$b$$ is not divisible by the square of any prime. What is the value of $$a + b +c$$?

Details and assumptions

$$f^{(n)} (x)$$ means that $$f$$ is applied $$n$$ times, e.g. $$f^{(2)} (x) = f \circ f (x) = f( f( x) )$$

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