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Chapter 13: Problem 24

Describe the region \(R\) in the \(x y\) -plane that corresponds to the domain of the function. $$ g(x, y)=\frac{1}{x-y} $$

Short Answer

Expert verified
The domain of the function is all points (x, y) in xy-plane except those points where x = y.

Step by step solution

01

Understand the Domain of a Function

Domain is defined as the set of all possible values of x that can be put into the given function without violating any mathematical rules. In this function, x can be any real number except when x = y.
02

Define the Expression for Domain

In the function g(x, y) = 1/(x-y), domain is undefined where x-y equals zero or simply x = y. Therefore, the domain of the function g is all set of points (x, y) in the xy-plane except those points where x = y.
03

Graph Representation

This domain can be represented graphically as the xy-plane excluding the line y = x.

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