# Function of several real variables

In mathematical analysis its applications, a **function of several real variables** or **real multivariate function** is a function with more than one argument, with all arguments being real variables. This concept extends the idea of a function of a real variable to several variables. The "input" variables take real values, while the "output", also called the "value of the function", may be real or complex. However, the study of the complex valued functions may be easily reduced to the study of the real valued functions, by considering the real and imaginary parts of the complex function; therefore, unless explicitly specified, only real valued functions will be considered in this article.

This article includes a list of general references, but it remains largely unverified because it lacks sufficient corresponding inline citations. (November 2017) |

Function |
---|

x ↦ f (x) |

Examples of domains and codomains |

Classes/properties |

Constructions |

Generalizations |

The domain of a function of *n* variables is the subset of **R**^{n} for which the function is defined. As usual, the domain of a function of several real variables is supposed to contain a nonempty open subset of **R**^{n}.