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Combinations of Functions; Composite Functions

Combinations of Functions; Composite Functions. Objectives. Students will be able to add, subtract, multiply and divide functions. Students will be able to find the composition of one function with another function.

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Combinations of Functions; Composite Functions

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  1. Combinations of Functions; Composite Functions

  2. Objectives • Students will be able to add, subtract, multiply and divide functions. • Students will be able to find the composition of one function with another function. • Students will be able to use combinations and composition of functions to model and solve real life problems.

  3. Let f and g be two functions. The sum of f + g, the differencef – g, the productfg, and the quotientf /g are functions whose domains are the set of all real numbers common to the domains of f and g, defined as follows: Sum: (f + g)(x) = f (x)+g(x) Difference: (f – g)(x) = f (x) – g(x) Product: (f • g)(x) = f (x) • g(x) Quotient: (f / g)(x) = f (x)/g(x), provided g(x) does not equal 0 Definitions: Sum, Difference, Product, and Quotient of Functions

  4. Let f(x) = 2x+1 and g(x) = x2-2. Find f + g, f - g, fg, and f/g and state the domain of each.. Solution: f+g = 2x+1 + x2-2 = x2+2x-1 f-g = (2x+1) - (x2-2)= -x2+2x+3 fg = (2x+1)(x2-2) = 2x3+x2-4x-2 f/g = (2x+1)/(x2-2) (f+g)(2) = (2)2+2(2)-1 = 7 Example

  5. The composition of the function f with g is denoted by fog and is defined by the equation (fog)(x) = f (g(x)). The domain of the composite function fog is the set of all x such that x is in the domain of g and g(x) is in the domain of f. See pg. 105 figure P.96 The Composition of Functions

  6. Given f (x) = 2x – 8 and g(x) = x2 - 5, find: a.(fog)(x) b. (gof)(x) What is the domain of each? Try Page 107 # 12, 16, 26, 28, 38, 42 Homework: Page 107 – 108 #9, 13, 15, 17, 21, 25, 27, 37 – 47 0dd Example

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