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2013 PUMaC Algebra B4

Source:

November 22, 2013
geometryfunction

Problem Statement

Let f(x)=1−∣x∣f(x)=1-|x|. Let \begin{align*}f_n(x)&=(\overbrace{f\circ \cdots\circ f}^{n\text{ copies}})(x)\\g_n(x)&=|n-|x| |\end{align*} Determine the area of the region bounded by the xx-axis and the graph of the function ∑n=110f(x)+∑n=110g(x).\textstyle\sum_{n=1}^{10}f(x)+\textstyle\sum_{n=1}^{10}g(x).
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