Let and Find each value or expression. See
Examples 5 and 6.
47. 48. 49. 50.
Solve each problem.
51.The function defined by computes the number of inches in xfeet, and the
function defined by computes the number of feet in xmiles. What is
and what does it compute?
52.The perimeter xof a square with sides of length sis given by the for-
mula
(a)Solve for sin terms of x.
(b)If yrepresents the area of this square, write yas a function of the
perimeter x.
(c)Use the composite function of part (b) to find the area of a square with perimeter 6.
53.When a thermal inversion layer is over a city (as hap-
pens often in Los Angeles), pollutants cannot rise verti-
cally, but are trapped below the layer and must disperse
horizontally. Assume that a factory smokestack begins
emitting a pollutant at 8 A.M. Assume that the pollutant
disperses horizontally over a circular area. Suppose that
trepresents the time, in hours, since the factory began
emitting pollutants ( represents 8 A.M.), and as-
sume that the radius of the circle of pollution is
Let represent the area of
a circle of radius r. Find and interpret
54.An oil well is leaking, with the leak spreading oil over the
surface as a circle. At any time t, in minutes, after the begin-
ning of the leak, the radius of the circular oil slick on the
surface is Let represent the
area of a circle of radius r. Find and interpret 1 ar 21 t 2.
r 1 t 2 = 4 t feet. a 1 r 2 =pr^2
1 ar 21 t 2.
r 1 t 2 = 2 t miles. a 1 r 2 =pr^2
t= 0
x= 4 s.
1 ƒg 21 x 2
g 1 x 2 = 5280 x
ƒ 1 x 2 = 12 x
1 gƒ2a-
1
2
1 ƒg2a- b
1
2
1 hƒ2a b
1
2
1 ƒh2a b
1
2
b
1 gƒ 21 x 2 1 gh 21 x 2 1 hg 21 x 2 1 hƒ 21 x 2
1 ƒh 21 - 22 1 hg 21 - 22 1 ƒg 2102 1 ƒh 2102
1 hg 2142 1 ƒg 2142 1 g ƒ 2162 1 hƒ 2162
ƒ 1 x 2 =x^2 +4, g 1 x 2 = 2 x+3, h 1 x 2 =x-5.
292 CHAPTER 5 Exponents, Polynomials, and Polynomial Functions
s
s
ss
r(t)
r(t)
Graph each function. Give the domain and range. See Example 7.
59.ƒ 1 x 2 =x^3 + 1 60.ƒ 1 x 2 =-x^3 + 2
ƒ 1 x 2 =
1
2
ƒ 1 x 2 =- 3 x^2 x^2
ƒ 1 x 2 =- 2 x+ 1 ƒ 1 x 2 = 3 x+ 2
Find each product. See Section 5.1.
- 12 x^2 y 15 xy^32 66. 6 mn^313 m^4 n 2
- 3 b^512 a^3 b^42 - 4 k^21 - 3 k^5 t^32
3 m^314 m^225 z^217 z^42
PREVIEW EXERCISES
