Not too Complicated

Algebra Level 4

Let f(x)=x1x+1f(x) = \frac{x-1}{x+1} and fn(x)f^{n}(x) denote the nfoldn-\text{fold} composition of ff with itself. That is, f1(x)=f(x)f^1(x) =f(x) and fn(x)=f(fn1(x))f^n(x) = f(f^{n-1}(x)). Find f2007(2)f^{2007}(2).

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