Section 1.8 Combinations of Functions Section 1.8 Combinations of Functions: Composite Functions Objective: In this lesson you learned how to find arithmetic combinations and compositions of functions. Course Number I. Arithmetic Combinations of Functions (Pages 76−77) Date Instructor Just as two real numbers can be combined with arithmetic operations, two functions can be combined by the operations of aaaaaaaaa aaaaaaaaaaaa aaaaaaaaaa aaa aaaaaaaa a to create new functions. A combined function like this is called What you should learn How to add, subtract, multiply, and divide functions an arithmetic combination of functions. The domain of an arithmetic combination of functions f and g consists of . . . aaa aaaa aaaaaaa aaaa aaa aaaaaa aa aaa aaaaaaa aa a aaa aa aa aaa aaaa aa aaa aaaaaaaa aaaaaaaaaa aaaaa aa aaa aaaaaaa aaaaaaaaaaa aaaa aaaa a aa Let f and g be two functions with overlapping domains. Complete the following arithmetic combinations of f and g for all x common to both domains: 1) Sum: ( f + g )( x ) = aaaa a aaaa a 2) Difference: 3) Product: 4) Quotient: Example: aaaa a aaaa ( f − g )( x ) = ( fg )( x) = f (x) = g a aaaa a aaaa aaaa aaaa aaaa a a a Let f ( x ) = 7 x − 5 and g ( x ) = 3 − 2 x . Find ( f − g )(4) . aa II. Composition of Functions (Pages 78−79) The composition of the function f with the function g is defined as ( f o g )( x ) = a aaaaaaa . What you should learn How to find the composition of one function with another function Chapter 1 Functions and Their Graphs For the composition of the function f with g, the domain of ( f o g ) is . . . aaa aaa aa aaa a aa aaa aaaaaa aa a aaaa aaaa aaaa aa aa aaa aaaaaa aa aa For two functions f and g, to find ( f o g )(x ) , . . . aaaaaaa aaaa aaaaaaaaaa aa a aa a aaaa aaa aaaaaaaaa aaaaaaaaaa aaaaa aaaaaaa aaaaa aaaa aaaaaaaaa Example: Let f ( x ) = 3x + 4 and let g ( x) = 2 x 2 − 1 . Find (a) ( f o g )(x ) and (b) ( g o f )(x ) . aaa aa a a a aaa aaa a a aaa a aa III. Application (Page 80) The function f ( x ) = 0.06 x represents the sales tax owed on a purchase with a price tag of x dollars and the function g ( x) = 0.75 x represents the sale price of an item with a price tag of x dollars during a 25% off sale. Using one of the combinations of functions discussed in this section, write the function that represents the sales tax owed on an item with a price tag of x dollars during a 25% off sale. aa aaaaa a aa aaaaa a aaaaaa Additional notes Homework Assignment Page(s) Exercises What you should learn How to use combinations of functions to model and solve real-life problems

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