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2002 AMC 12A Problem 19

Problem 19 of 25HarderAlgebra

The graph of the function ff is shown below. How many solutions does the equation f(f(x))=6f(f(x)) = 6 have?

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Solution

The graph reaches 66 at x=−2x = -2 and x=1,x = 1, so f(f(x))=6f(f(x)) = 6 requires f(x)=−2f(x) = -2 or f(x)=1.f(x) = 1. The horizontal line y=−2y = -2 meets the graph twice, and y=1y = 1 meets it four times, giving 2+4=62 + 4 = 6 solutions. Thus, the correct answer is D.

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Concepts: function · data and graph interpretation

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