On uncertain functions
In this paper, we analize some basic properties of the real functions f : R → R that satisfy the polynomial equation X 2 + 1 = 0 (that is, such that f2 + idR = 0, where f2 = f ◦ f). We prove their existence, give a characterization of such functions and show a concrete example from which infinite ot...
Guardado en:
| Autores principales: | , |
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| Formato: | Artículo revista |
| Lenguaje: | Español |
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Unión Matemática Argentina - Facultad de Matemática, Astronomía, Física y Computación
2023
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| Materias: | |
| Acceso en línea: | https://revistas.unc.edu.ar/index.php/REM/article/view/41052 |
| Aporte de: |
| Sumario: | In this paper, we analize some basic properties of the real functions f : R → R that satisfy the polynomial equation X 2 + 1 = 0 (that is, such that f2 + idR = 0, where f2 = f ◦ f). We prove their existence, give a characterization of such functions and show a concrete example from which infinite other examples can be derived. Next, we discuss some issues about their continuity. Finally, a classic linear algebra mechanism allows us to prove that, for every polynomial P ∈ Q[X], there exist functions f : R → R that satisfy the polynomial equation P = 0. |
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