Functions of Two or More Independent Variables

Abstract

We recall the formula

$$ \begin{array}{*{20}c} {z = (xy)^{\frac{1}{2}} } \hfill & {(x \geqq 0,\,y \geqq 0)} \hfill \\ \end{array} $$

((12.1.1))

for the geometric mean of two numbers x and y. Consider x and y as variables whose values can be chosen independently of each other. Then with each pair (x, y) there is uniquely associated a number z, the geometric mean. In Chapter 3 we called such an association a function. We say that z is a function of the pair (x, y), or the pair (x, y) is mapped into z. It is also customary to call z a function of two variables x and y.