# Definition:Real Function/Multivariable

## Definition

Let $f: S_1 \times S_2 \times \cdots \times S_n \to \R$ be a mapping where $S_1, S_2, \ldots, S_n \subseteq \R$.

Then $f$ is defined as a (real) function of $n$ (independent) variables.

The expression:

$y = f \left({x_1, x_2, \ldots, x_n}\right)$

means:

(The dependent variable) $y$ is a function of (the independent variables) $x_1, x_2, \ldots, x_n$.

## Also see

• Results about real functions can be found here.