C Challenge

Find the inverse of each function. Is the inverse a function?

68. f ( x ) = 1 5 x 3 f , open x close , equals , 1 fifth , x cubed
69. f ( x ) = x − 5 3 f , open x close , equals . cube root of x minus 5 end root ,
70. f ( x ) = x 3 3 f , open x close , equals , fraction cube root of x , , over 3 end fraction
71. f ( x ) = ( x − 2 ) 3 f open x close equals . open x minus 2 close cubed
72. f ( x ) = x 4 f , open x close , equals , the fourth , root of x ,
73. f ( x ) = 1.2 x 4 f open x close equals 1.2 , x to the fourth
74. Function f(x) is defined the following way:
    • if x is an integer, then f(x) = x + 1;

    • for all other x, f(x) = x + 2.

      Is the inverse of f(x) a function? Explain.

Standardized Test Prep

SAT/ACT

75. Which pair of words make this sentence FALSE?

    The product of two ___________(I)___________ numbers is always a (n) ___________(II)___________ number.

    1. (I) complex; (II) complex
    2. (I) real; (II) complex
    3. (I) rational; (II) real
    4. (I) imaginary; (II) imaginary
76. If f(x) = x + 1 and g ( x ) = x 2 − 3 x − 4 , g open x close equals , x squared , minus 3 x minus 4 comma  what is ( f ∘ g ) ( x ) ? open f composition g close open x close question mark
    6. x 2 − 3 x − 3 x squared , minus 3 x minus 3
    7. x 2 − x − 6 x squared , minus x minus 6
    8. x 2 − x x squared , minus x
    9. x 2 − x − 3 x squared , minus x minus 3
77. What is the simplified form of ( a 2 3 b 3 4 ) 2 ? open . eh super 2 thirds end super . b super 3 fourths end super . close squared . question mark
    1. a 4 9 b 9 16 eh super 4 ninths end super . b super 9 sixteenths end super
    2. a 4 3 b 3 2 eh super 4 thirds end super . b super 3 halves end super
    3. ab
    4. ( a b ) 17 6 open , eh b , close super 17 over 6 end super

Extended Response

78. Let f ( x ) = ( x + 1 ) 2 − 2 . f open x close equals . open x plus 1 close squared . minus 2 .  Find the x- and y-intercepts of f(x) and the inverse of f(x). Is the inverse a function?

Mixed Review

See Lesson 6-6.

Let f(x) = 4 x , g ( x ) = 1 2 x + 7 , g , open x close , equals , 1 half , x plus 7 comma  and h ( x ) = − 2 x + 4 . h open x close equals negative 2 x plus 4 .  Perform each function operation.

79. ( g ∘ f ) ( x ) open g composition f close open x close
80. ( h ∘ g ) ( x ) open h composition g close open x close
81. h ( x ) + g ( x ) h open x close plus g open x close
82. f ( x ) · g ( x ) f open x close middle dot g open x close
83. ( f ∘ g ) ( x ) + h ( x ) open f composition g close open x close plus h open x close
84. ( f ∘ g ) ( x ) open f composition g close open x close

See Lesson 6-1.

Find each real root.

85. − 16 4 negative , the fourth , root of 16 ,
86. − 16 4 the fourth , root of negative 16 end root ,
87. 243 5 the fifth , root of 243 ,
88. − 243 5 negative , the fifth , root of 243 ,
89. − 243 5 the fifth , root of negative 243 end root ,
90. 0.064 3 cube root of 0.064 ,
91. 810 , 000 4 the fourth , root of 810 comma 000 end root ,
92. 1 160 , 000 4 the fourth , root of fraction 1 , over 160 comma 000 end fraction end root ,

Get Ready! To prepare for Lesson 6-8, do Exercises 93–95.

See Lesson 4-1.

Graph each function.

93. y = − x 2 − 1 y equals negative , x squared , minus 1
94. y = − ( x + 1 ) 2 + 1 y equals negative . open x plus 1 close squared . plus 1
95. y = 3 x 2 + 3 y equals , 3 x squared , plus 3

Table of Contents