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Chapter 11: Problem 23

Describe the domain and range of the function. $$ z=\frac{x+y}{x y} $$

Short Answer

Expert verified
The domain of the function \( z=\frac{x+y}{x y} \) is all real numbers except for those which make the denominator of the function zero, and the range is all real numbers.

Step by step solution

01

Identify the function

The provided function is \( z=\frac{x+y}{x y} \). This function is defined for every ordered pair (x, y), except those for which x*y equals zero.
02

Define the domain

The domain of this function is all real numbers excluding the values for which x*y equals zero. In precise, the domain for x and y is \( X = \{x \in \mathbb{R}: x \neq 0\} \) and \( Y = \{y \in \mathbb{R}: y \neq 0\} \).
03

Define the range

The range of the function is all real numbers since there are no restrictions on z in the original equation.

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