College Algebra 9th txtbk

SECTION 3–1 Functions 173
27. Let f(x) 3x 5. Find
(A) f(3)
(B) f(h)
(C) f(3) f(h) (D) f(3 h)
28. Let g(y) 7 2y. Find
(A) g(4)
(B) g(h)
(C) g(4) g(h) (D) g(4 h)
29. Let F(w) w 2 2w. Find
(A) F(4)
(B) F(4)
(C) F(4 a) (D) F(2 a)
30. Let G(t) 5t t 2 . Find
(A) G(8)
(B) G(8)
(C) G(1 h) (D) G(6 t)
31. Let f(t) 2 3t 2 . Find
(A) f(2) (B) f(t)
(C) f(t)
(D) f(t)
32. Let k(z) 40 20z 2 . Find
(A) k(2) (B) k(z)
(C) k(z) (D) k(z)
33. Let F(u) u 2 u 1. Find
(A) F(10) (B) F(u 2 )
(C) F(5u) (D) 5F(u)
34. Let G(u) 4 3u u 2 . Find
(A) G(8) (B) G(u 2 )
(C) G(2u) (D) 2G(u)
Problems 35–36 refer to the following graph of a function f.
10
f(x)
10
y f(x)
10
x
In Problems 47–62, find the domain of the indicated function.
Express answers in both interval notation and inequality notation.
47. f(x) 4 9x 3x 2 48. g(t) 1 7t 2t 2
49. L(u) 23u 2 4 50.
53. g(t) 1t 4 54. h(t) 16 t
55. k(w) 17 3w 56. j(w) 19 4w
57. H(u)
u
58. G(u)
u
u 2 4
u 2 4
59. M(x) 1x 4 60.
x 1
M(w) w 5
23 2w 2
51. h(z) 2
52. k(z)
z
4 z
z 3
N(x) 1x 3
x 2
1
1
61. s(t)
62. r(t)
3 1t
1t 4
The verbal statement “function f multiplies the square of the
domain element by 3 and then subtracts 7 from the result” and the
algebraic statement “f(x) 3x 2 7” define the same function. In
Problems 63–66, translate each verbal definition of a function into
an algebraic definition.
63. Function g subtracts 5 from twice the cube of the domain
element.
64. Function f multiplies the square of the domain element by 10
then adds 1,000 to the result.
65. Function F multiplies the square root of the domain element
by 8, then subtracts the product of 4 and the sum of the domain
element and two.
66. Function G divides the sum of the domain element and 7 by
the cube root of the domain element.
10
35. (A) Find f(2) to the nearest integer.
(B) Find all values of x, to the nearest integer, so that f (x) 4.
36. (A) Find f(4) to the nearest integer.
(B) Find all values of x, to the nearest integer, so that f (x) 0.
Determine which of the equations in Problems 37–46 define a
function with independent variable x. For those that do, find the
domain. For those that do not, find a value of x to which there
corresponds more than one value of y.
37. y x 2 1 38. y 2 x 1
39. 2x 3 y 2 4 40. 3x 2 y 3 8
41. x 3 y 2 42. x 3 y 6
43. 2x y 7 44. y 2x 3
45. 3y 2|x| 12 46. x| y| x 1
In Problems 67–70, translate each algebraic definition of the
function into a verbal definition.
67. f(x) 2x 2 5 68. g(x) 2x 7
69. z(x) 4x 5
70. M(t) 5t 21t
1x
F(2 h) F(2)
71. If F(s) 3s 15, find:
h
K(1 h) K(1)
72. If K(r) 7 4r, find:
h
g(3 h) g(3)
73. If g(x) 2 x 2 , find:
h
P(2 h) P(2)
74. If P(m) 2m 2 3, find:
h