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12. f(x) = 2x-5, 14. f(x) = 2x - 5, g(x) = 1 - x g(x) = 5 16. fƒ(x) = √x² − 4, g(x) = - = x² x² + 1

12. f(x) = 2x-5, 14. f(x) = 2x - 5, g(x) = 1 - x g(x) = 5 16. fƒ(x) = √x² − 4, g(x) = - = x² x² + 1

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Finding Arithmetic Combinations of Functions In Exercises 11-18, find (a) (f+g)(x), (b) (f- g)(x), . (c) (fg)(x), and (d) (f/g)(x). What is the domain of flg? 12. f(x)=2x-5, g(x) = 1 - x 14. f(x) = 2x - 5, g(x) = 5 16. f(x)=√√x² - 4, g(x) Evaluating an Arithmetic Combination of Functions In Exercises 19-32, evaluate the indicated function for f(x)=x²-1 and g(x) = x - 2 algebraically. If possible, use a graphing utility to verify your answer. 20. (ƒ - g)(-2) 22. (f + g)(1) 24. (fg)(-4) 26. (f/g)(0) BAA Compositions of Functions In Exercises 41-44, find (a) fog, (b) gof, and, if possible, (c) (fog)(0). x² x² + 1 41. f(x) = x², g(x) = x - 1 42. f(x) = 3√x-1, g(x) = x³ + 1 43. f(x) = 3x + 5, g(x) = 5x 44. f(x) = x³, g(x) = X 71. h(x) = (2x + 1)² 73. h(x) = 3x² - 4 Identifying a Composite Function In Exercises 71-78, find two functions f and g such that (fog)(x) = h(x). (There are many correct answers.) 72. h(x) = (1-x)³ 74. h(x) = √√9 - x
Transcribed Image Text:Finding Arithmetic Combinations of Functions In Exercises 11-18, find (a) (f+g)(x), (b) (f- g)(x), . (c) (fg)(x), and (d) (f/g)(x). What is the domain of flg? 12. f(x)=2x-5, g(x) = 1 - x 14. f(x) = 2x - 5, g(x) = 5 16. f(x)=√√x² - 4, g(x) Evaluating an Arithmetic Combination of Functions In Exercises 19-32, evaluate the indicated function for f(x)=x²-1 and g(x) = x - 2 algebraically. If possible, use a graphing utility to verify your answer. 20. (ƒ - g)(-2) 22. (f + g)(1) 24. (fg)(-4) 26. (f/g)(0) BAA Compositions of Functions In Exercises 41-44, find (a) fog, (b) gof, and, if possible, (c) (fog)(0). x² x² + 1 41. f(x) = x², g(x) = x - 1 42. f(x) = 3√x-1, g(x) = x³ + 1 43. f(x) = 3x + 5, g(x) = 5x 44. f(x) = x³, g(x) = X 71. h(x) = (2x + 1)² 73. h(x) = 3x² - 4 Identifying a Composite Function In Exercises 71-78, find two functions f and g such that (fog)(x) = h(x). (There are many correct answers.) 72. h(x) = (1-x)³ 74. h(x) = √√9 - x
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