Implicit function

In mathematics, an implicit equation is a binary relation of the form R(x1,..., xn) = 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.

The implicit function theorem provides conditions under which a relation defines an implicit function.

See also

• Functional equation
• Function (mathematics)
• Level set
• Contour line
• Isosurface
• Marginal rate of substitution
• Implicit function theorem
  • Logarithmic differentiation
  • Polygonizer

External links

• Implicit function @ Wikipedia.org