Buy Precalculus Function Skills Discussion

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Basic Function Concepts
66. Indicate whether the statement is true or false. Explain your reasoning.
(A) {(–4,5),(–1,5),(0,5),(5,5)} is a function.
(B) {(x, y) | y = 2x} is a function.
(C) If (4,a) and (4,b) are elements of a function, then a = b.
(D) The domain of a function is a subset of that function.
(E) In the function f = {(x,y) | y = 5x 3},y = f(x) is the image of x under f.
For questions 67 to 73, evaluate and simplify as indicated.
67. when f(x) = 28x – 10
68. y = f(–5) when f (x) = x
2 1
69. y = f(–1) when f (x) = 4x
5 2x
4 –3x
3 –5x
2 x 5
70. when
71. y = f(3) when
72. f(5x) when
73. f (x
2 1) when
For questions 74 to 78, find the domain, Df
, and range, Rf
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, for the given realvalued functions. Note: In a real-valued function both the domain and range of
the function consist of real numbers. All functions in this chapter are real-valued.
74. f defined by
75.
76. g defined by
77. h defined by h(x) = | 7x – 2 |
78. f defined by
Operations with Functions
For questions 79 to 82, using and g(x) = x
4
, write a simplified expression
for the indicated function. Refer to the following definitions, as needed.
For all real numbers x such that x ∈ Df ∩ Dg
:
(f g)(x) = f (x) g(x);
(f – g)(x) = f (x) – g(x);
(fg)(x) = f (x) · g(x); and
, where g(x) ≠ 0.
79. (f g)(x)
80. (f – g)(x)
81. (fg)(x)
82. (x)
For questions 83 to 86, using f (x) = x
2 3 and
g(x) = – 3, evaluate (if possible).
83. (f g)(4)
84. (f – g)(6)
85. (fg)(–1)
86. (9)
87. Let f = {(–5,1),(–4,–3),(–1,3),(2,5),(6,–4)} and
g = {(–4,2),(–3,–3),(–1,3),(1,9),(3,–4)}; (a) find f g and (b) determine (f
g)(–4) (if possible).
88. Let f = {(–5,1),(–4,–3),(–1,3),(2,5),(6,–4)} and
g = {(–4,2),(–3,–3),(–1,3),(1,9),(3,–4)}; (a) find g f and (b) determine (g
f)(6) (if possible).
89. Let f = {(–2,–8),(–1,3),(0,1),(1,4),(2,8)} and
g = {(–2,–7),(–1,4),(0,–2),(1,2),(2,0),(3,8)}; (a) find f g and (b) determine
(f g)(1) (if possible).
90. Let f = {(–2,–8),(–1,3),(0,1),(1,4),(2,8)} and
g = {(–2,–7),(–1,4),(0,–2),(1,2),(2,0),(3,8)}; (a) find g f and (b) determine
(g f)(2) (if possible).
For questions 91 to 95, use the given f (x) and g(x) to (a) write a simplified
expression for (f g)(x) and (b) determine the domain of f g.
91. and g(x) = 3x
2
92. f (x) = | x | and g(x) = 9x – 4
93. f (x) = and g(x) = 16x
2
94. f (x) = and g(x) = 5x
95. and g(x) = 1–12x
For questions 96 to 100, use and g(x) = x
2 4 to evaluate each
expression (if possible).
96. (f g)(9)
97. (f g)(0)
98. (f g)(40)
99. (f g)(10)
100. (g f)(5)
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For questions 101 to 105, determine whether the function is one-to-one.
101. f = {(1,4),(2,5),(3,6),(4,7),(5,8)}
102.
103.
104. f = {(x, y) | y = 1}
105.
106. If f = {(0,1),(1,5),(2,9),(3,13)}, find f
–1
.
For questions 107 to 111,find an equation that defines the inverse of the given
function.
107. y = f (x) = 3x 1
108. y = g(x) = (x 5)
3
109. h(x) = 7x
110.
111. y = f (x) = x
2
, where the domain of f = {x | x ≥ 0}
For questions 112 to 115, evaluate f
–1(x) at the value x for the function f defined
as indicated.
112. f = {(0,1),(1,5),(2,9),(3,13)}, x = 9
113. f (x) = (x – 32), x = 0
114. f (x) = x 5, x = 0.5
115.
For questions 116 to 120,determine whether the function f is even, odd, or
neither.
116. f (x) = x
3
117. g(x) = | x 3 |
118. h(x) = 36x
2 – 10
119. g(x) = 2x
2 – x 1
120. f (x) = 3x
4 – l0x
2 8
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