2015 Special

Algebra Level 5

If f 1 ( x ) = ∣ ∣ x ∣ − 2 ∣ f_{1}(x)=||x|-2| and f n ( x ) = ∣ f n − 1 ( x ) − 2 ∣ f_{n} (x) =|f_{n-1}(x)-2| for all n ≥ 2 n \geq 2 , n ∈ N n \in \mathbb N . Then find number of solutions of the equation f 2015 ( x ) = 2 f_{2015}(x)=2 .


The answer is 2017.

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Shubhendra Singh by Shubhendra Singh , 20, India

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1 solution

Draw the graph of the function |x-2| Then to draw ||x-2|-2| Using transformation of graphs we notice that the 1st function has 3 real solutions and the number of solutions increase by 1. Therefore we arrive at the conclusion that number of solutions is 2017.

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