Implicit function

In mathematics, an implicit equation is a relation of the form R(x₁,..., x_n) = 0, where R is a function of several variables (often a polynomial). For example, the implicit equation of the unit circle is $x^2 +y^2-1 = 0.$

An implicit function is a function that is defined implicitly by an implicit equation, by associating one of the variables (the value) with the others (the arguments). Thus, an implicit function for y in the context of the unit circle is defined implicitly by $x^2 +[f(x)]^2-1 = 0.$ . This implicit equation defines f as a function of x only if -1 ≤ x ≤ 1 and one considers only non-negative (or non-positive) values for the values of the function.

单词	Implicit equation
释义	Implicit equation 英语百科 Implicit function In mathematics, an implicit equation is a relation of the form R(x₁,..., x_n) = 0, where R is a function of several variables (often a polynomial). For example, the implicit equation of the unit circle is $x^2 +y^2-1 = 0.$ An implicit function is a function that is defined implicitly by an implicit equation, by associating one of the variables (the value) with the others (the arguments). Thus, an implicit function for y in the context of the unit circle is defined implicitly by $x^2 +[f(x)]^2-1 = 0.$ . This implicit equation defines f as a function of x only if -1 ≤ x ≤ 1 and one considers only non-negative (or non-positive) values for the values of the function.
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Implicit equation

Implicit function