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Function Iteration

Source: 1986 National High School Mathematics League, Exam One, Problem 8

February 24, 2020
function

Problem Statement

f(x)=∣1−2x∣,x∈[0,1]f(x)=|1-2x|,x\in[0,1]. Then the number of solutions to f(f(f(x)))=12xf(f(f(x)))=\frac{1}{2}x is________.
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