If f(x)=11−xf(x) = \frac{1}{1-x}f(x)=1−x1, find the 202420242024-th iterate f2024(x)f_{2024}(x)f2024(x).
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11−x\frac{1}{1-x}1−x1
x−1x\frac{x-1}{x}xx−1
1−x1-x1−x