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MathNet 2007-part-02 — 187 problems (EN–VI) Question 153

Math Olympiad Vault · MathNet 2007-part-02 — 187 problems (EN–VI)

Question 153

Consider the function $f$ defined by
$$
f(x) = 1 + \frac{2}{x}
$$
Find the roots of the equation
$$
(\underbrace{f \circ f \circ \cdots \circ f}_{10 \text{ times}})(x) = x
$$
where "o" denotes composition of functions.