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1.8 Combinations of Functions: Composite Functions

84 Chapter 1 Functions and Their GraphsArithmetic Combinations of FunctionsJust as two real numbers can be combined by the operations of addition, subtrac-tion, multiplication, and division to form other real numbers, two functionscan becombined to create new Functions . For example, the Functions given byand can be combined to form the sum, difference,product, and quotient of and SumDifferenceProductQuotientThe domain of an arithmetic combinationof Functions and consists of allreal numbers that are common to the domains of and In the case of the quo-tient there is the further restriction that Finding the Sum of Two FunctionsGiven and find SolutionNow try Exer

When the food is removed from refrigeration, the temperature of the food is given by where is the time in hours. (a) Find the composition and interpret its meaning in context. (b) Find the time when the bacterial count reaches 2000. Solution a. The composite function represents the number of bacteria in the food

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