244
Chapter 2 Graphs and Functions
(b)
f ( x h) f ( x) 1 2 x 2 4 xh 2h 2 1 2 x 2
58. g x x 3 g 2 2 3 1
f
1 2 x 2 4xh 2h 2 1 2x 2 4 xh 2h 2 f ( x h) f ( x)
4xh 2h
21 3 2 3 1 59. g x x 3 g 2 2 3 5
2
(c) h
f
60.
2
61.
f ( x h) x h 3 x h 1
f 3
g3 3 3 0
f x 2x 3 f 0 2 0 3 0 3 3 f 0
g f0 g
2
62.
x 3x 1 2
f 3 23 3 6 3 3
g3
33 33 6
f ( x h) f ( x) x 2 2xh h 2 3x 3h 1 2
f x 2x 3 g f3 g
x 2 2 xh h 2 3x 3h 1 (b)
f5
2 5 3 10 3 7
f ( x) x 2 3x 1
(a)
g 2 f g 2
h h(4x 2h) h 4 x 2h
55.
g 2 f g 2 f 1
f x 2x 3 f 2 2 2 3 7 g f 2 g f 2 g 7 7 3 7 3 10
2
x 2 xh h 3x 3h 1 x 3x 1 2 xh h 2 3h
f x 2x 3 f 2 2 2 3 4 3 1 63.
f ( x h) f ( x) (c)
h
2xh h 2 3h
f
h(2x h 3) h
g g 2 g g 2
f ( x) x 2 4 x 2 (a)
(b)
2
f ( x h) x h 4 x h 2 x 2 2 xh h 2 4 x 4h 2 f ( x h) f ( x) x 2 2xh h 2 4x 4h 2
x2 4 x 2 x 2 2 xh h 2 4 x 4h 2 x 2 4 x 2 2 xh h 2 4h
(c)
f ( x h) f ( x) 2 xh h 2 4h h h h(2x h 4) h 2x h 4
f 2
f 1 21 3 1
64. g x x 3 g 2 2 3 5
2x h 3
56.
f2 f
h
g5 5 3 2
65. ( f
g)(2) f [ g (2)] f (3) 1
66. ( f
g)(7) f [ g (7)] f (6) 9
67. ( g f )(3) g[ f (3)] g (1) 9 68. ( g f )(6) g[ f (6)] g (9) 12
69. ( f
f )(4) f [ f (4)] f (3) 1
70. ( g g)(1) g[ g (1)] g (9) 12 71. ( f g)(1) f [ g (1)] f (9) However, f (9) cannot be determined from the table given. 72. ( g ( f
g))(7) g ( f ( g (7))) g ( f (6)) g (9) 12
73. (a) ( f g)(x) f ( g ( x)) f (5x 7)