Dictionary

implicit function en · NOUN

Pronunciation

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Meanings

1. A function defined by a (multivariable) implicit equation when one of the variables is regarded as the value of the function, especially where said equation is such that the value is not directly calculable from the other variables.
   • In this section we discuss the analysis of implicit functions for addressing questions like this. 2002, Michael W. Klein, Mathematical Methods for Economics, Addison-Wesley, page 245:
   • An important class of implicit functions comprises those defined by equations of the form x-f(y)#61;0. Choosing y as the value means that the implicit function is the inverse of f. This type of implicit function is of particular interest when that inverse is not expressible as a closed-form expression, and thus is difficult to study directly.
   • The process of evaluating the derivatives in the case of implicit functions is exemplified below. 1875, J. Minot Rice, W. Woolsey Johnson, The Elements of the Differential Calculus, Part 2, Washington: Government Printing Office, page 71:
   • Thus, in the equation, #92;quad#92;quad#92;quaday²#43;bxy#43;cx²#43;d#61;0; y is an implicit function of x. Implicit functions are generally connected with their variables by one or more equations. When these equations are solved the implicit equation becomes explicit. […]The differential of an implicit function may be found without first finding the function itself. 1871, William G. Peck, Practical Treatise on the Differential and Integral Calculus, A. S. Barnes & Company, page 50:

Forms

Relateds

implicit differentiation · algebraic function · implicit equation · functional equation · explicit function · implicit curve · implicit function theorem

Translations (8)

bg неявна функция (function defined as the solution to an implicit equation) · tl hiwatig na kabisa (function defined as the solution to an implicit equation) · es función implícita (function defined as the solution to an implicit equation) · de implizite Funktion (function defined as the solution to an implicit equation) · ru нея́вная фу́нкция (function defined as the solution to an implicit equation) · it funzione implicita (function defined as the solution to an implicit equation) · fr fonction implicite (function defined as the solution to an implicit equation) · is fólgið fall (function defined as the solution to an implicit equation)