**INTRODUCTION** Two functions *f* and *g* can be combined in several ways to create new functions. In this section we will examine two such ways in which functions can be combined: through arithmetic operations, and through the operation of function composition.

**Arithmetic Combinations** Two functions can be combined through the familiar four arithmetic operations of addition, subtraction, multiplication, and division.

DEFINITION 2.6.1 Arithmetic Combinations

If *f* and *g* are two functions, then the **sum** *f* + *g*, the **difference** *f* − *g*, the **product** *fg*, and the **quotient** *f*/*g* are defined as follows:

EXAMPLE 1 **Sum, Difference, ...**

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