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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