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2011 PUMaC Algebra A5

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September 24, 2019
algebra

Problem Statement

Let f_1(x) = \frac{1}{x} \text{and}  f_2(x) = 1 - x Let HH be the set of all compositions of the form h1∘h2∘…∘hkh_1 \circ h_2 \circ \ldots \circ h_k, where each hih_i is either f1f_1 or f2f_2. For all hh in HH, let h(n)h^{(n)} denote hh composed with itself nn times. Find the greatest integer NN such that π,h(π),…,h(N)(π)\pi, h(\pi), \ldots, h^{(N)}(\pi) are all distinct for some hh in HH.
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