248
95.
Chapter 2 Graphs and Functions
f
gx f g x
5 1 x3
4
x3 4 4
3
3
3
1
5x 4 5 5x 5
96.
f
f
5
g x f g x f 1760 x 3 1760 x 5280 x
34
5x 4
5 4 5x 4 4 5
5
f g x compute the number of feet in x miles.
5
5
x 105. 3
x3 1 1
3
f x
g fx g
f x 3x, g x 1760 x
5
13
g x f g x 3
5
x3 x
f x
g fx g
104.
4
3
x 11
x3 x
( x) 4
3
x2 3
(2 x)
(a)
4
3
3
x1 1
x 11 x In Exercises 97−102, we give only one of many possible answers.
3 (4 x 2 ) 4
3x 2
3 (8) 2 (16) A(2 8) 64 3 square units
(b)
x
106. (a) x 4s
2
97. h( x) (6 x 2) Let g(x) = 6x – 2 and
(2 x) 2
2
(b) y s
s 4s
x 4
2
2
4 x
16 x
f ( x) x 2 . ( f g )( x) f (6 x 2) (6 x 2) 2 h( x) 98. h( x) (11x 2 12 x) 2 Let g ( x) 11x 2 12x and f ( x) x 2 . (f
g)(x) f (11x 2 12 x) (11x 2 12 x) 2 h( x)
99. h( x)
y
62 16
2 107. (a) r (t ) 4t and (r) r ( r)(t) [r(t )] (4t ) (4t )
g)(x) f ( x 2 1)
x.
(c)
x 2 1 h( x).
Let g ( x) 2x 3 and f ( x) x3 . g)(x) f (2 x 3) (2 x 3)3 h( x)
108. (a) (
102. h( x)
f ( x)
g)(x) f (6x) 3
x 12.
6x 12 h( x)
2x 3 4
Let g ( x) 2x 3 and f ( x) (f
r)(t)
[r(t )] (2t ) (2t )
2
4 t2
r)(4) 4 (4) 2 64 mi 2
6x 12
Let g ( x) 6 x and (f
16 t 2
(b) It defines the area of the circular layer in terms of the time t, in hours. (c) (
101. h( x)
2
(3) 16 (3) 2 144 ft 2
3 100. h( x) (2x 3)
(f
36 2.25 square units 16
(b) ( r)(t) defines the area of the leak in terms of the time t, in minutes.
x2 1
Let g ( x) x 2 1 and f ( x) (f
(c)
g)(x) f (2 x 3)
3
3
x 4.
2x 3 4 h( x)
103. f(x) = 12x, g(x) = 5280x ( f g)(x) f [ g ( x)] f (5280x) 12(5280 x) 63, 360x The function f g computes the number of inches in x miles.
109. Let x = the number of people less than 100 people that attend. (a) x people fewer than 100 attend, so 100 – x people do attend N(x) = 100 – x (b) The cost per person starts at $20 and increases by $5 for each of the x people that do not attend. The total increase is $5x, and the cost per person increases to $20 + $5x. Thus, G(x) = 20 + 5x. (c) C ( x) N ( x) G( x) (100 x)(20 5x)
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