f(f(x))= -x, Windmills and Beyond

• Autores: Martin Griffiths
• Localización: Mathematics magazine, ISSN 0025-570X, Vol. 83, Nº. 1, 2010, págs. 15-23
• Idioma: inglés
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• Resumen

  • In this article we consider the solutions of a particular functional equation and some generalizations. This equation possesses non-trivial yet accessible solutions, and is rather appealing because of the way that the enforced graphical symmetry of any solution implies that it must possess a certain non-obvious analytic property. Indeed, a central theme here is this interplay of the visual with the analytic aspects of the problem. After giving a brief historical overview of functional equations, we go on to study the general properties shared by functions satisfying our particular equation, as well as specific solutions. Finally, solutions to a generalization of the equation are obtained.