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Suppose the graph of \(y=f(x)\) includes the points (1,5), (2,3), and (3,1). Based only on this information, there are two points that must be on the graph of \(y=f(f(x))\). If we call those points (a,b) and (c,d), what is \(ab+cd\)?

 Nov 14, 2019
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Since \(f(f(2))=f(3)=1\)and \(f(f(3))=f(1)=5\), the two points on the graph of \(y=f(f(x))\) must be \((2, 1) \) and \((3, 5)\). So ab + cd = 2 + 15 = 17.

 Nov 14, 2019

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