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Find (a) f(g(x)), (b) g(f(x)), and (c)f(f(x)). State the domain and range of each composition. 56. f(x)= 3x², g(x) = -x-2 57. f(x) = 6x + 5, g(x)=√x + 4 3, 50 co

Find (a) f(g(x)), (b) g(f(x)), and (c)f(f(x)). State the domain and range of each composition. 56. f(x)= 3x², g(x) = -x-2 57. f(x) = 6x + 5, g(x)=√x + 4 3, 50 co

Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter2: Functions
Section2.2: Graphs Of Functions
Problem 84E
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Solve the problem number 57 and show your work
Performing Function Operations (pp. 279-284) Learning Target: Perform arithmetic operations on two functions. Find (f+g)(x) and (f- g)(x) and state the domain of each. Then evaluate f + g and f-g for the given value of x. 48. f(x) = 3(5), g(x) = -8(5*); x = 4 Find (fg)(x) and (²) (x) and state the domain given value of .x. 50. f(x) = 2x4 + 3, g(x) = x -2; x = − 1 51. f(x) = x² + 5x - 16, g(x) = x³ + x²; x = 3 Determine whether the statement is always, sometimes, or never true. Explain your reasoning. 52. For two quadratic functions fand g, f + g is also a quadratic function. 53. For two functions f and g, when f(a) = 3 and g(a) = 4, (fg)(a) = 12. 5.6 5.7 ▶ WATCH Composition of Functions (pp. 285-290) Learning Target: Evaluate and find compositions of functions. Use the functions f(x) = x²-3, g(x) = x + 6, and h(x) = the table. x- 2 54. X 5 7 9 11 13 g(h(x)) 49. f(x) = 3x² + 1, g(x) = x +4; x = -5 of each. Then evaluate fg and I for the g 56. f(x) = 3x², g(x) = -x - 2 58. f(x) = -7x + 1, g(x)=√x - 2 55. WATCH X -6 -4 -2 0 2 to complete 62. You have the coupons shown to use for a purchase at an online store. Use a composition of functions to determine which coupon you should apply first. Explain. f(g(x)) Find (a) f(g(x)), (b) g(f(x)), and (c)f(f(x)). State the domain and range of each composition. 57. f(x) = 6x + 5, g(x)=√x + 4 59. f(x)=x-9, g(x) = x³ - 4x +3 60. Let f(x) = 4x - 3, g(x) = -x² + 8, and h(x) = -x. Find (a) g(h(x)), (b) f(g(h(x))), and (c) f(g(h(4))). What do you notice about g(h(x))? 61. Let f be a radical function and let g be a linear function with a nonzero slope. What type of function results when you compose f and g? Vocabulary composition Online Coupons $15 OFF 10% OFF ENTIRE PURCHASE ENTIRE PURCHASE Use coupon code 15DOLLARSOFF Use coupon code 10PERCENTOFF GO DIGIT 口口
Transcribed Image Text:Performing Function Operations (pp. 279-284) Learning Target: Perform arithmetic operations on two functions. Find (f+g)(x) and (f- g)(x) and state the domain of each. Then evaluate f + g and f-g for the given value of x. 48. f(x) = 3(5), g(x) = -8(5*); x = 4 Find (fg)(x) and (²) (x) and state the domain given value of .x. 50. f(x) = 2x4 + 3, g(x) = x -2; x = − 1 51. f(x) = x² + 5x - 16, g(x) = x³ + x²; x = 3 Determine whether the statement is always, sometimes, or never true. Explain your reasoning. 52. For two quadratic functions fand g, f + g is also a quadratic function. 53. For two functions f and g, when f(a) = 3 and g(a) = 4, (fg)(a) = 12. 5.6 5.7 ▶ WATCH Composition of Functions (pp. 285-290) Learning Target: Evaluate and find compositions of functions. Use the functions f(x) = x²-3, g(x) = x + 6, and h(x) = the table. x- 2 54. X 5 7 9 11 13 g(h(x)) 49. f(x) = 3x² + 1, g(x) = x +4; x = -5 of each. Then evaluate fg and I for the g 56. f(x) = 3x², g(x) = -x - 2 58. f(x) = -7x + 1, g(x)=√x - 2 55. WATCH X -6 -4 -2 0 2 to complete 62. You have the coupons shown to use for a purchase at an online store. Use a composition of functions to determine which coupon you should apply first. Explain. f(g(x)) Find (a) f(g(x)), (b) g(f(x)), and (c)f(f(x)). State the domain and range of each composition. 57. f(x) = 6x + 5, g(x)=√x + 4 59. f(x)=x-9, g(x) = x³ - 4x +3 60. Let f(x) = 4x - 3, g(x) = -x² + 8, and h(x) = -x. Find (a) g(h(x)), (b) f(g(h(x))), and (c) f(g(h(4))). What do you notice about g(h(x))? 61. Let f be a radical function and let g be a linear function with a nonzero slope. What type of function results when you compose f and g? Vocabulary composition Online Coupons $15 OFF 10% OFF ENTIRE PURCHASE ENTIRE PURCHASE Use coupon code 15DOLLARSOFF Use coupon code 10PERCENTOFF GO DIGIT 口口
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