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Essentials of Precalculus with Calculus Previews, 6th Edition by Zill

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2.6    Combining Functions

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.

ImagesArithmetic 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 fg, the product fg, and the quotient f/g are defined as follows:

EXAMPLE  1      Sum, Difference, ...

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