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f(x) f(k - x) > 0

Source: 2001 Cuba MO 2.1

September 15, 2024
inequalitiesalgebra

Problem Statement

Let ff be a linear function such that f(0)=−5f(0) = -5 and f(f(0))=−15f(f(0)) = -15. Find the values of k∈R k \in R for which the solutions of the inequality f(x)⋅f(k−x)>0f(x) \cdot f(k - x) > 0, lie in an interval of length 22.
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