2012 AIME II Problems/Problem 11

Revision as of 16:10, 31 March 2012 by Williamhu888 (talk | contribs) (Created page with "== Problem 11 == Let <math>f_1(x) = \frac23 - \frac3{3x+1}</math>, and for <math>n \ge 2</math>, define <math>f_n(x) = f_1(f_{n-1}(x))</math>. The value of <math>x</math> that sa...")
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Problem 11

Let $f_1(x) = \frac23 - \frac3{3x+1}$, and for $n \ge 2$, define $f_n(x) = f_1(f_{n-1}(x))$. The value of $x$ that satisfies $f_{1001}(x) = x-3$ can be expressed in the form $\frac mn$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$.

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