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Chapter 12: Q 1. (page 915)

Explain why Definition 0.1 is general enough to include functions of two and three variables.

Short Answer

Expert verified

Each combination of real numbers (x, y) in the domain of a function f of two different variables is assigned a real number f(x, y).

Step by step solution

01

Step 1. Given information

Term "function" is given.

02

Step 2. Explanation

Definition 0.1 is as follows:

A function from a set A to set B is an assignment f that associates to each element x of the domain of set A exactly one element f(x) of the codomain or target set B

Each combination of real numbers (x, y) in the domain of a function f of two different variables is assigned a real number f(x, y).

Each combination of real numbers (x, y, z) in the domain of a function f of three different variables is assigned a real number f(x, y, z).

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