Exercise Set 2.4

Vocabulary Review 1. c 2. e 3. d 4. a 5. bProblems 1. 6x + 2 3. −2x + 8 5. 8x2 + 14x − 15

7. 2x + 5_____4x − 3 9._ 3x − 5 + 5_

x 11._ 5_x − 3x + 5 13. 15 − 25__

x15. 5______

3x 2x − 5x 17._ 4x − 7 19. 3x2 − 10x + 8 21. −2x + 3

23. 3x2 − 11x + 10 25. 9x3 − 48x2 + 85x − 50 27. x − 229. 1____

x − 2 31. 3x2 − 7x + 3 33. 6x2 − 22x + 20, ℝ

35. 4x − 7 _ 3x 2−11x + 10

, D = (−∞, 5_3 ) ∪ ( 5_

3 , 2 ) ∪ (2, ∞)

37. 9x2 − 30x + 25, D = All real numbers 39. 8x2 − 26x + 21, D = All real numbers 41. 15 43. 98 45. 3_

247. 1 49. 40 51. 147 53. a. 81 b. 29 c. (x + 4)2 d. x2 + 455. a. −2 b. −1 c. 16x2 + 4x − 2 d. 4x2 + 12x − 1 57. a. 1 b. 1_

3 c. 9__x2 d. 3__

x2

59. ( f ∘ g)(gg x) = 5 (x + 4____5 ) − 4 61. ( f ∘ g)(gg x) = 3 (x_

3 − 2) + 6= x + 4 − 4 = x − 6 + 6= x = x

( g ∘ f )(x) = (5x − 4) + 4_________5 ( g ∘ f )(x) = 3x + 6_____

3 − 2= 5x__

5 = x + 2 − 2= x = x

63. –1 65. −4_3 67._ 2_

5 69._ −2 71. 2_7

73. a. R(x) = 11.5x − 0.05x2 b. C(x) = 2x + 200c. P(x) = −0.05x2xx + 9.5x − 200 d.

__C (x) = 2 + 200___

x75. a. M(x) = 220 − x b. x M(24) = 196 c. 142 d. 135 e. 12877. a. Coal: f(ff x) = 94.80x, Wind: g(x) = 97.00x

b. c. h(x) = 3.20x

79. a. Coal: f(ff x) = 136.20x, Wind: g(x) = 97.00x b. c. h(x) = 39.20x

81. 12 83. 28 85. −7_4 87._ w = P − 2l_____

2

89. [–6, ∞)

91.

60

(–∞, 6)

93. 6, 2 95. ∅

Find the Mistake 1. Th e function (f (( + g ) (x) is the sum of thefunctions f (x) and g (x). 2. Th e function ( f_

g) (x) = f (x)

___ g(x) .

3. If f (x) = 3x + 4 and g (x) = x − 3, the function(f (( + g ) (x) = (3x + 4) + (x − 3) or 4x + 1.4. For (f (( ∘ g ) (x) the numbers in the domain of the compositefunction must be numbers in the domain of ff ff

Landmark Review1. 2.

3. 4.

5. Domain = {4, 3, 1, 7}; Range = {3, 2, 9}; A function 6. Domain = {0, 1, 3}; Range = {3, 4, 2}; Not a function7. Domain = {a, 4, b, 5 }; Range = {0, 3, 1}; A function8. Domain = {1}; Range = {3, 5, 2, 0}; Not a function 9. 510. 12 11. 3a − 1 12. a 2 + 9a + 20 13. 5x − 4 14. x − 6 15. 6x2 − 7x − 5 16. 3x − 5_____

2x + 1 17. −3 18. 16

0 20 40 60 80 1000

5,000

10,000

dollars

Dollars

mWh

g(x)

f(x)

(100, 9,700)

(100, 9,480)

0 20 40 60 80 1000

5,000

10,000

dollars

Dollars

mWh

g(x)

f(x)

(100, 13,620)

(100, 9,480)

�6 0

x

y

x

y

x

y

x

y