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Recursive functions with absolute value

Source: Poland Math Olympiad 1993 Round 1 #2

June 3, 2023
functionabsolute value

Problem Statement

The sequence of functions f0,f1,f2,...f_0,f_1,f_2,... is given by the conditions: f0(x)=∣x∣f_0(x) = |x| for all x∈Rx \in R fn+1(x)=∣fn(x)−2∣f_{n+1}(x) = |f_n(x)-2| for n=0,1,2,...n=0,1,2,... and all x∈Rx \in R. For each positive integer nn, solve the equation fn(x)=1f_n(x)=1.
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