The Inverse of a cubic function

Motivated by a question asked by an undergraduate student we determine when the cubic function f(x) = x3 + ax, with a being a real number, is bijective in its domain. For this purpose we use some basic results from calculus and by using a formula for the solution of the cubic equation x3 + mx = n fo...

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Autores principales: Carena, Marilina, Toledano, Ricardo
Formato: Artículo revista
Lenguaje:Español
Publicado: Unión Matemática Argentina - Facultad de Matemática, Astronomía, Física y Computación 2024
Materias:
Función inversa
Polinomio cúbico
Raíces
Inverse function
Roots
Cubic polynomial function
Acceso en línea:https://revistas.unc.edu.ar/index.php/REM/article/view/46291
Aporte de:
Revista de Educación Matemática de Universidad Nacional de Córdoba
id I10-R366-article-46291
record_format ojs
spelling I10-R366-article-462912024-08-30T15:56:20Z The Inverse of a cubic function La inversa de una función cúbica Carena, Marilina Toledano, Ricardo Función inversa Polinomio cúbico Raíces Inverse function Roots Cubic polynomial function Motivated by a question asked by an undergraduate student we determine when the cubic function f(x) = x3 + ax, with a being a real number, is bijective in its domain. For this purpose we use some basic results from calculus and by using a formula for the solution of the cubic equation x3 + mx = n found by Cardano in the 16th century, we find an explicit expression for the inverse function of f Motivados por la pregunta de un alumno de primer año de universidad, determinamos cuando la función cúbica f(x) = x+ax, donde a es un número real, es biyectiva en su dominio. Para ello utilizamos algunos resultados basicos del cálculo y, con la ayuda de la resolvente de la ecuación cúbica x3 + mx = n hallada por Cardano a mediados del siglo XVI, encontramos una expresión explícita para la funcion inversa de f. Unión Matemática Argentina - Facultad de Matemática, Astronomía, Física y Computación 2024-08-30 info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Artículo evaluado por pares application/pdf https://revistas.unc.edu.ar/index.php/REM/article/view/46291 10.33044/revem.46291 Revista de Educación Matemática; Vol. 39 Núm. 2 (2024); 5-17 1852-2890 0326-8780 spa https://revistas.unc.edu.ar/index.php/REM/article/view/46291/46483 https://creativecommons.org/licenses/by-sa/4.0/
institution Universidad Nacional de Córdoba
institution_str I-10
repository_str R-366
container_title_str Revista de Educación Matemática
language Español
format Artículo revista
topic Función inversa
Polinomio cúbico
Raíces
Inverse function
Roots
Cubic polynomial function
spellingShingle Función inversa
Polinomio cúbico
Raíces
Inverse function
Roots
Cubic polynomial function
Carena, Marilina
Toledano, Ricardo
The Inverse of a cubic function
topic_facet Función inversa
Polinomio cúbico
Raíces
Inverse function
Roots
Cubic polynomial function
author Carena, Marilina
Toledano, Ricardo
author_facet Carena, Marilina
Toledano, Ricardo
author_sort Carena, Marilina
title The Inverse of a cubic function
title_short The Inverse of a cubic function
title_full The Inverse of a cubic function
title_fullStr The Inverse of a cubic function
title_full_unstemmed The Inverse of a cubic function
title_sort inverse of a cubic function
description Motivated by a question asked by an undergraduate student we determine when the cubic function f(x) = x3 + ax, with a being a real number, is bijective in its domain. For this purpose we use some basic results from calculus and by using a formula for the solution of the cubic equation x3 + mx = n found by Cardano in the 16th century, we find an explicit expression for the inverse function of f
publisher Unión Matemática Argentina - Facultad de Matemática, Astronomía, Física y Computación
publishDate 2024
url https://revistas.unc.edu.ar/index.php/REM/article/view/46291
work_keys_str_mv AT carenamarilina theinverseofacubicfunction
AT toledanoricardo theinverseofacubicfunction
AT carenamarilina lainversadeunafuncioncubica
AT toledanoricardo lainversadeunafuncioncubica
AT carenamarilina inverseofacubicfunction
AT toledanoricardo inverseofacubicfunction
first_indexed 2024-09-03T22:37:02Z
last_indexed 2024-09-03T22:37:02Z
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