# Implicit

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### Random information on the term “Implicit”:

In mathematics, an implicit equation is a relation of the form R ( x 1 , … , x n ) = 0 {\displaystyle R(x_{1},\ldots ,x_{n})=0} , where R {\displaystyle 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 {\displaystyle 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).:204–206 Thus, an implicit function for y {\displaystyle y} in the context of the unit circle is defined implicitly by x 2 + f ( x ) 2 − 1 = 0 {\displaystyle x^{2}+f(x)^{2}-1=0} . This implicit equation defines f {\displaystyle f} as a function of x {\displaystyle x} only if − 1 ≤ x ≤ 1 {\displaystyle -1\leq x\leq 1} and one considers only non-negative (or non-positive) values for the values of the function.