HMMT November 2008 U24

Let $f(x)=\frac{1}{1-x}$ . Let $f^{k+1}(x)=f\left(f^{k}(x)\right)$ , with $f^{1}(x)=f(x)$ . What is $f^{2008}(2008)$ ?

Dataset text NuminaMath olympiads. Quoted with source.

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\frac{-1}{2007}

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