MathDB
TOT 377 1993 Spring A S5 piecewise linear function f(f(x)) = -x

Source:

June 10, 2024
functionalgebrafunctionalfunctional equation

Problem Statement

Does there exist a piecewise linear function ff defined on the segment [−1,1]-1,1] (including the ends) such that f(f(x))=−xf(f(x)) = -x for all x? (A function is called piecewise linear if its graph is the union of a finite set of points and intervals; it may be discontinuous).
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