Deck 1: Preparing for Calculus

Question 1

Let $f ( x ) = - | x | + 5$ Then $f ( - x )$ is

A) $- | x | + 5$
B) $- | x | - 5$
C) $| x | + 5$
D) $| x | - 5$
E) $- | x + 5 |$

Answer 1

$- | x | + 5$

Question 2

Let $f ( x ) = \sqrt { 6 - 5 x }$ Then $f ( x + 1 )$ is

A) $\sqrt { 5 - 5 x }$
B) $\sqrt { 7 - 5 x }$
C) $\sqrt { 7 + 5 x }$
D) $\sqrt { 1 - 5 x }$
E) $\sqrt { 1 + 5 x }$

Answer 2

$\sqrt { 1 - 5 x }$

Question 3

Let $f ( x ) = \frac { 2 x + 3 } { x ^ { 2 } - 1 }$ Then $- f ( x )$ is

A) $\frac { 2 x + 3 } { x ^ { 2 } - 1 }$
B) $\frac { - 2 x - 3 } { x ^ { 2 } - 1 }$
C) $\frac { - 2 x + 3 } { x ^ { 2 } - 1 }$
D) $\frac { - 2 x + 3 } { x ^ { 2 } + 1 }$
E) $\frac { 3 - 2 x } { x ^ { 2 } - 1 }$

Answer 3

$\frac { - 2 x - 3 } { x ^ { 2 } - 1 }$

Question 4

Let $f ( x ) = - 5 x + 2$ Then $\frac { f ( x + h ) - f ( x ) } { h }$ is

A)-1
B)1
C)-5
D)5
E)-5 + h

Question 5

Let $f ( x ) = x ^ { 2 } - x$ Then $\frac { f ( x + h ) - f ( x ) } { h }$ is

A)-1
B)1
C)x+ h
D)2x+ h
E)2x- 1 + h

Question 6

Let $f ( x ) = \frac { 1 } { x - 1 }$ Then $\frac { f ( x + h ) - f ( x ) } { h }$ is

A)1
B) $\frac { - 1 } { ( x - 1 ) ^ { 2 } }$
C) $\frac { 1 } { ( x - 1 ) ^ { 2 } }$
D) $\frac { 1 } { ( x + h - 1 ) ( x + 1 ) }$
E) $\frac { - 1 } { ( x + h - 1 ) ( x - 1 ) }$

Question 7

Let $f ( x ) = \sqrt { 4 - x }$ Then $\frac { f ( x + h ) - f ( x ) } { h }$ is

A)1
B) $\frac { - 1 } { \sqrt { 4 - x - h } }$
C) $\frac { 1 } { \sqrt { 4 - x - h } + \sqrt { 4 - x } }$
D) $- \frac { 1 } { \sqrt { 4 - x - h } + \sqrt { 4 - x } }$
E) $- \frac { 1 } { \sqrt { 4 - x + h } + \sqrt { 4 - x } }$

Question 8

Let $f ( x ) = 2 | x | - 3$ Then f is

A)an odd function
B)an even function
C)neither an even nor an odd function
D)an increasing function
E)a decreasing function

Question 9

Let $f ( x ) = x - 2 x ^ { 3 }$ Then f is

A)an odd function
B)an even function
C)neither an even nor an odd function
D)an increasing function
E)a decreasing function

Question 10

The rate of change of $f ( x ) = \frac { 2 } { x - 3 }$ from 2 to 5 is

A)1
B)-1
C) $- \frac { 3 } { 2 }$
D) $\frac { 3 } { 2 }$
E) $\frac { 5 } { 3 }$

Question 11

The rate of change $f ( x ) = \sqrt { 5 - x }$ from x = 1 to x = 4 is

A)1
B)-1
C) $- \frac { 1 } { 3 }$
D) $\frac { 1 } { 3 }$
E) $\frac { 5 } { 3 }$

Question 12

The domain of the function $f ( x ) = \frac { 3 } { 2 x ^ { 2 } - 5 x - 3 }$ is

A) $\left( - \frac { 1 } { 2 } , 3 \right)$
B) $\left( - \infty , - \frac { 1 } { 2 } \right) \cup ( 3 , \infty )$
C) $( - \infty , - 3 ) \cup \left( - 3 , \frac { 1 } { 2 } \right)$
D) $( - \infty , - 3 ) \cup \left( - 3 , \frac { 1 } { 2 } \right) \cup \left( \frac { 1 } { 2 } , \infty \right)$
E) $\left( - \infty , - \frac { 1 } { 2 } \right) \cup \left( - \frac { 1 } { 2 } , 3 \right) \cup ( 3 , \infty )$

Question 13

The domain of the function $f ( x ) = \sqrt { 2 x + 3 }$ is

A) $( - \infty , \infty )$
B) $\left( - \frac { 3 } { 2 } , \infty \right)$
C) $\left[ - \frac { 3 } { 2 } , \infty \right)$
D) $\left( - \frac { 2 } { 3 } , \infty \right)$
E) $\left[ \frac { 3 } { 2 } , \infty \right)$

Question 14

The domain of the function $f ( x ) = \sqrt { x ^ { 2 } - 4 }$ is

A) $( - \infty , \infty )$
B)(-2,2)
C) $[ - 2,2 ]$
D) $( - \infty , - 2 ) \cup ( 2 , \infty )$
E) $( - \infty , - 2 ] \cup [ 2 , \infty )$

Question 15

If $f ( x ) = \left\{ \begin{array} { c l } 2 x - 5 & x < - 4 \\\frac { x } { 2 } & x \geq - 4\end{array} \right.$ , then $f ( - 4 )$ is

A) $- 13$
B)-8
C)-2
D)3
E)8

Question 16

If $f ( x ) = \left\{ \begin{array} { c c } - 2 x + 1 & - 3 \leq x < - 1 \\4 & - 1 < x \leq 5 \\x - 2 & 5 < x < 7\end{array} \right.$ , then

A) $f ( - 3 ) = - 5$
B) $f ( - 1 ) = 4$
C) $f ( 5 ) = 4$
D) $f ( 5 ) = 3$
E) $f ( 7 ) = 5$

Question 17

If $f ( x ) = \left\{ \begin{array} { c c } x ^ { 2 } - 1 & - 3 \leq x < 0 \\3 x & 0 \leq x < 3 \\2 x - 5 & 3 \leq x < 10\end{array} \right.$ , then

A) $f ( - 3 ) = - 10$
B) $f ( 0 ) = - 1$
C) $f ( 0 ) = 0$
D) $f ( 3 ) = 9$
E) $f ( 3 ) = 8$

Question 18

If $f ( x ) = \left\{ \begin{array} { c c } \frac { x - 1 } { x ^ { 2 } + 1 } & - 2 \leq x < 1 \\3 x & 3 \leq x < 6 \\10 - 7 x & 7 < x < 10\end{array} \right.$ then

A) $f ( - 2 ) = 3$
B) $f ( 1 ) = 0$
C) $f ( 3 ) = 9$
D) $f ( 6 ) = 18$
E) $f ( 10 ) = 60$

Question 19

If $f ( x ) = \left\{ \begin{array} { c c } - 2 x + 1 & - 3 \leq x < - 1 \\4 & - 1 < x < 5, \\x - 2 & 5 < x < 7\end{array} \right.$ then the domain of f is

A) $[ - 3,7 ]$
B) $[ - 3,7 )$
C) $( - 3 , - 1 ) \cup ( - 1,7 )$
D) $[ - 3 , - 1 ) \cup ( - 1,7 ]$
E) $[ - 3 , - 1 ) \cup ( - 1,5 ) \cup ( 5,7 )$

Question 20

If $f ( x ) = \left\{ \begin{array} { c l } x ^ { 2 } - 1 & - 3 \leq x < 0 \\3 x & 0 \leq x < 3 \\2 x - 5 & 3 \leq x < 10\end{array} \right.$ then the domain of f is

A) $[ - 3,10 ]$
B) $[ - 3,10 )$
C) $( - 3,0 ) \cup ( 0,10 )$
D) $[ - 3,3 ) \cup ( 3,10 ]$
E) $[ - 3,0 ) \cup ( 3,10 )$

Question 21

If $f ( x ) = 2 x$ , then $f ( - 2.8 )$ is

A)-6
B)-5.6
C)-4
D)4
E)6

Question 22

If $f ( x ) = - \lfloor x \rfloor + 4$ , then $f ( - 5.1 )$ is

A)-2
B)-1
C)9
D)9.1
E)10

Question 23

If $f ( x ) = \lfloor - 3 x \rfloor$ , then $f ( 2.5 )$ is

A)-7
B)-8
C)-9
D)7
E)8

Question 24

If $f ( x ) = \left\lceil \frac { x } { 3 } \right\rceil$ , then $f ( - 1.5 )$ is

A)-1
B)-0.5
C)0
D)0.5
E)1

Question 25

If $f ( x ) = 2 x - 3 x$ , then $f ( 3.2 )$ is

A)-3
B)-1
C)1
D)3
E)4

Question 26

If $f ( x ) = 3 \lceil x \rceil + 4 \lceil x \rceil$ , then $f ( - 1.6 )$ is

A)-11
B)-10
C)-9
D)-8
E)-7

Question 27

The domain of $f ( x ) = \frac { 4 x - 6 } { x ^ { 2 } + 9 }$ is

A) $( - \infty , \infty )$
B) $( - \infty , - 3 )$
C) $( - 3,3 )$
D) $( 3 , \infty )$
E) $( - \infty , - 3 ) \cup ( 3 , \infty )$

Question 28

The domain of $f ( x ) = \frac { 3 x - 2 } { 9 x ^ { 2 } - 4 }$ is

A) $\left( - \infty , - \frac { 2 } { 3 } \right)$
B) $\left( - \infty , \frac { 2 } { 3 } \right)$
C) $\left( - \frac { 2 } { 3 } , \frac { 2 } { 3 } \right)$
D) $\left( - \infty , - \frac { 2 } { 3 } \right) \cup \left( \frac { 2 } { 3 } , \infty \right)$
E) $\left( - \infty , - \frac { 2 } { 3 } \right) \cup \left( - \frac { 2 } { 3 } , \frac { 2 } { 3 } \right) \cup \left( \frac { 2 } { 3 } , \infty \right)$

Question 29

The set of all x-intercepts of $f ( x ) = \frac { x ^ { 2 } - x - 6 } { x ^ { 2 } + x - 6 }$ is

A){-3,-2}
B){-3,2}
C){-6,1}
D){-2,3}
E){-1,6}

Question 30

The set of all x-intercepts of $f ( x ) = \frac { x ^ { 2 } - x } { x ^ { 2 } + 5 x - 6 }$ is

A){0}
B){0,1}
C){-1,0}
D){-6,1}
E){-1,6}

Question 31

The set of all x-intercepts of $f ( x ) = \frac { 2 x + 3 } { 2 x ^ { 2 } + x - 3 }$ is

A) $\varnothing$
B) $\left\{ - \frac { 3 } { 2 } , 1 \right\}$
C) $\left\{ - \frac { 3 } { 2 } \right\}$
D) $\left\{ - 1 , \frac { 3 } { 2 } \right\}$
E){1}

Question 32

The set of all x-intercepts of $f ( x ) = \lceil x \rceil + 1$ is

A) $( - 2 , - 1 ]$
B) $( - 2 , - 1 )$
C){-1}
D){-2}
E) $[ - 2 , - 1 )$

Question 33

The set of all x-intercepts of $f ( x ) = \left\lfloor \frac { x } { 2 } \right\rfloor$ is

A) $( 0,1 ]$
B) $( 0,2 )$
C) $[ 0,2 )$
D) $[ 0,2 ]$
E) $[ 1,2 )$

Question 34

The set of all x-intercepts of $f ( x ) = \lceil x \rceil - 1$ is

A) $( 0,1 ]$
B) $[ 0,1 )$
C) $[ 1,2 )$
D) $(1,2)$
E) $( 1,2 ]$

Question 35

Which of the following is a constant function?

A) $f ( x ) = 2 x ^ { 2 } - 5$
B) $f ( x ) = \frac { 1 } { e }$
C) $f ( x ) = \frac { 1 } { x }$
D) $f ( x ) = 2 x + 7$
E) $f ( x ) = \sqrt { x }$

Question 36

Which of the following is a constant function?

A) $f ( x ) = \frac { 1 } { \pi ^ { 2 } }$
B) $f ( x ) = x ^ { 6 } + 1$
C) $f ( x ) = x + 6$
D) $f ( x ) = | x |$
E) $f ( x ) = \sqrt { x }$

Question 37

Which of the following is a polynomial function?

A) $f ( x ) = x ^ { 3 / 2 } + x - 1$
B) $f ( x ) = \frac { 3 } { 2 } x ^ { 2 } - 2 - \frac { 1 } { x }$
C) $f ( x ) = 3 x - 4$
D) $f ( x ) = \frac { x } { 2 } + \frac { 3 } { x ^ { 2 } }$
E) $f ( x ) = \frac { x ^ { 2 } - x + 1 } { x }$

Question 38

Which of the following is a polynomial function?

A) $f ( x ) = \frac { \lfloor x \rfloor } { 2 }$
B) $f ( x ) = | x | + 2$
C) $f ( x ) = 3 \lceil x \rceil$
D) $f ( x ) = - \frac { x } { 5 }$
E) $f ( x ) = \sqrt { 5 x }$

Question 39

Which of the following is a rational function?

A) $f ( x ) = x ^ { 3 / 2 } - 1 + \frac { 1 } { x }$
B) $f ( x ) = \frac { x ^ { 2 } - 1 } { 5 x - 6 }$
C) $f ( x ) = \sqrt { | x | + 6 }$
D) $f ( x ) = 8 x + \sqrt [ 3 ] { x }$
E) $f ( x ) = \frac { 5 x } { \sqrt { x ^ { 2 } + 1 } }$

Question 40

Which of the following is a rational function?

A) $f ( x ) = \frac { \lfloor x \rfloor + 3 } { x - 2 }$
B) $f ( x ) = \frac { | x | ^ { 2 } + 5 } { x + 1 }$
C) $f ( x ) = \frac { \sqrt { x } - 5 } { \sqrt { x - 5 } }$
D) $f ( x ) = \frac { 1 } { 2 } x ^ { 2 } + \frac { 5 } { \sqrt { x } }$
E) $f ( x ) = \frac { 3 } { 2 } x ^ { 2 } - \frac { 11 } { x }$

Question 41

Let $f ( x ) = 1 + \frac { 1 } { x }$ and $g ( x ) = \frac { 1 } { x }$ Which of the following is incorrect?

A) $( f + g ) ( - 1 ) = - 1$
B) $( f - g ) ( - 1 ) = - 1$
C) $( g - f ) ( - 1 ) = - 1$
D) $( f g ) ( - 1 ) = 0$
E) $\frac { f } { g } ( - 1 ) = 0$

Question 42

Let $f ( x ) = \sqrt { x - 1 }$ and $g ( x ) = \frac { 2 } { x }$ Which of the following is incorrect?

A) $( f + g ) ( 2 ) = 2$
B) $( f - g ) ( 2 ) = 0$
C) $( f g ) ( 2 ) = 1$
D) $\frac { f } { g } ( 2 ) = 1$
E) $\frac { g } { f } ( 1 ) = 1$

Question 43

Let $f ( x ) = 2 | x |$ and $g ( x ) = x$ Which of the following is incorrect?

A) $( f + g ) ( 0.5 ) = 1$
B) $( f - g ) ( 0.5 ) = 1$
C) $( g f ) ( 0.5 ) = 0$
D) $\frac { f } { g } ( 0.5 ) = 0$
E) $\frac { g } { f } ( 0.5 ) = 0$

Question 44

Let $f ( x ) = \frac { 3 } { x + 2 }$ and $g ( x ) = \left| x ^ { 2 } + 1 \right|$ Which of the following is incorrect?

A) $( f + g ) ( - 1 ) = 5$
B) $( f - g ) ( - 1 ) = - 1$
C) $( g f ) ( - 1 ) = 6$
D) $\frac { f } { g } ( - 1 ) = \frac { 3 } { 2 }$
E) $\frac { g } { f } ( 1 ) = 2$

Question 45

Let $f ( x ) = \pi$ and $g ( x ) = e + 3$ Which of the following is incorrect?

A) $( f + g ) ( 0 ) = \pi + e + 3$
B) $( f - g ) ( 0 ) = \pi - e + 3$
C) $( g - f ) ( 0 ) = e + 3 - \pi$
D) $\frac { f } { g } ( 0 ) = \frac { \pi } { e + 3 }$
E) $\frac { g } { f } ( 0 ) = \frac { e + 3 } { \pi }$

Question 46

Let $f ( x ) = 2 \pi$ and $g ( x ) = e + 3$ Which of the following is correct?

A) $( f + g ) ( 0 ) = 2 \pi + 6$
B) $( f - g ) ( 0 ) = 2 \pi - e + 3$
C) $( g - f ) ( 0 ) = 5 - 2 \pi$
D) $\frac { f } { g } ( 0 ) = \frac { \pi } { 5 }$
E) $\frac { g } { f } ( 0 ) = \frac { 6 } { \pi }$

Question 47

Let $f ( x ) = x + \frac { 1 } { x }$ and $g ( x ) = \frac { 1 } { x }$ Then $( f \circ g ) ( - 1 )$ is

A)-1
B)0
C)1
D)-2
E)2

Question 48

Let $f ( x ) = \sqrt { x - 1 }$ and $g ( x ) = \frac { 2 } { x }$ Then $( g \circ f ) ( 2 )$ is

A)-2
B)-1
C)0
D)1
E)2

Question 49

Let $f ( x ) = 2 | x |$ and $g ( x ) = \lfloor x \rfloor$ Then $( f \circ g ) ( - 0.5 )$ is

A)-2
B)-1
C)0
D)1
E)2

Question 50

Let $f ( x ) = 2 \pi$ and $g ( x ) = e + 3$ Then $( g \circ f ) ( 0 )$ is

A) $2 \pi$
B)5
C)6
D)7
E) $2 \pi ( e + 3 )$

Question 51

Let $f ( x ) = 2 \pi$ and $g ( x ) = e + 3$ The domain of $f \circ g$ is

A) $( - \infty , \infty )$
B) $( - \infty , 2 \pi ]$
C) $( - \infty , 0 )$
D) $( - \infty , 0 ]$
E) $[ 0 , \infty )$

Question 52

Let $f ( x ) = 2 \pi$ and $g ( x ) = \frac { 5 } { e + 3 }$ The domain of $g \circ f$ is

A) $( - \infty , \infty )$
B) $( - \infty , - 3 ) \cup ( - 3 , \infty )$
C) $( - \infty , 2 \pi ) \cup ( 2 \pi , \infty )$
D) $( - \infty , - 2 \pi ) \cup ( - 2 \pi , \infty )$
E) $( - \infty , e ) \cup ( e , \infty )$

Question 53

Let $f ( x ) = x + \frac { 1 } { x }$ and $g ( x ) = \frac { 1 } { x }$ Then the domain of $g \circ f$ is

A) $( - \infty , 0 ) \cup ( 0 , \infty )$
B) $( - \infty , - 1 ) \cup ( - 1 , \infty )$
C) $( - \infty , - 1 ) \cup ( 0 , \infty )$
D) $( - \infty , - 1 ) \cup ( - 1,0 )$
E) $( - \infty , - 1 ) \cup ( - 1,0 ) \cup ( 0 , \infty )$

Question 54

Let $f ( x ) = 2 | x |$ and $g ( x ) = \lfloor x \rfloor$ Then the domain of
Fog
Is

A) $( - \infty , \infty )$
B) $( - \infty , 0 )$
C) $( 0 , \infty )$
D) $( - \infty , 0 ]$
E) $[ 0 , \infty )$

Question 55

Let $f ( x ) = \sqrt { x - 1 }$ and $g ( x ) = \frac { 2 } { x }$ Then the domain of $f \circ g$ is

A) $[ 1 , \infty )$
B) $( 0,2 ]$
C) $[ 1,2 ]$
D) $( 0,1 ] \cup ( 2 , \infty )$
E) $[ 1 , \infty )$ .

Question 56

Let $f ( x ) = \sqrt { x - 1 }$ and $g ( x ) = \frac { 2 } { x }$ Then the domain of $g \circ f$ is

A) $[ 1 , \infty )$
B) $( 1 , \infty )$
C) $( 0 , \infty )$
D) $( 0,1 ) \cup ( 1 , \infty )$
E) $[ 0 , \infty )$

Question 57

Let $f ( x ) = 2 \pi$ and $g ( x ) = \frac { 5 } { e + 3 }$ Then $( f \circ g ) ( x )$ is

A) $\frac { 5 } { e + 3 }$
B) $2 \pi$
C) $\frac { 10 \pi } { e + 3 }$
D) $\frac { 5 } { 2 \pi ( e + 3 ) }$
E) $\frac { 5 } { 2 \pi + e + 3 }$

Question 58

Let $f ( x ) = \sqrt { 3 x - 4 }$ and $g ( x ) = 5 x + 6$ Then $( f \circ g ) ( x )$ is

A) $5 \sqrt { 3 x - 4 }$
B) $\sqrt { 15 x + 20 }$
C) $\sqrt { 15 x - 20 }$
D) $\sqrt { 15 x + 14 }$
E) $\sqrt { 15 x - 22 }$

Question 59

Let $f ( x ) = \sqrt { 3 x - 4 }$ and $g ( x ) = 5 x + 6$ Then $( g \circ f ) ( x )$ is

A) $5 \sqrt { 3 x - 4 } + 6$
B) $\sqrt { 15 x + 20 }$
C) $\sqrt { 15 x - 20 }$
D) $\sqrt { 15 x + 14 }$
E) $\sqrt { 15 x - 22 }$

Question 60

Let $f ( x ) = 3 + \frac { 1 } { x }$ and $g ( x ) = 3 - \frac { 1 } { x }$ Then $( g \circ f ) ( x )$ is

A) $\frac { 8 x - 35 } { 3 x + 1 }$
B) $\frac { 8 x + 3 } { 3 x + 1 }$
C) $\frac { 9 x + 3 } { 3 x + 1 }$
D) $\frac { 9 x - 3 } { 3 x + 1 }$
E) $\frac { 10 x + 3 } { 3 x + 1 }$

Question 61

Which of the following functions is one-to-one?

A) $f ( x ) = | x |$
B) $g ( x ) = x ^ { 2 }$
C) $h ( x ) = 6$
D) $F ( x ) = x - 6$
E) $G ( x ) = \lfloor x \rfloor$

Question 62

Which of the following functions is one-to-one?

A) $f ( x ) = | x - 2 |$
B) $g ( x ) = - x ^ { 2 } + 5$
C) $h ( x ) = \frac { 1 } { \pi }$
D) $F ( x ) = \lceil x \rceil$
E) $G ( x ) = x ^ { 3 }$

Question 63

Which of the following functions is one-to-one?

A) $f ( x ) = \frac { 1 } { x + 1 }$
B) $g ( x ) = 2 x ^ { 2 } - 3 x + 1$
C) $h ( x ) = e ^ { 3 }$
D) $F ( x ) = - 5 | x |$
E) $G ( x ) = - \lfloor x \rfloor$

Question 64

Which of the following functions is one-to-one?

A) $f ( x ) = \frac { 1 } { e }$
B) $g ( x ) = \lfloor x - 1 \rfloor + 2$
C) $h ( x ) = \sqrt { x }$
D) $F ( x ) = 2 | x | + 3$
E) $G ( x ) = - \lfloor x \rfloor$

Question 65

Which of the following functions is one-to-one?

A) $f ( x ) = 2 e + 1$
B) $g ( x ) = \sqrt [ 3 ] { x }$
C) $h ( x ) = - x ^ { 2 }$
D) $F ( x ) = - | x |$
E) $G ( x ) = - \frac { 1 } { x ^ { 2 } }$

Question 66

Which of the following functions is one-to-one?

A) $f ( x ) = \lfloor x \rfloor + 2$
B) $g ( x ) = \frac { 1 } { ( x - 3 ) ^ { 2 } }$
C) $h ( x ) = ( 2 x - 1 ) ^ { 2 }$
D) $F ( x ) = \frac { 3 } { x } - 6$
E) $G ( x ) = | x |$

Question 67

The function $f ( x ) = ( x + 1 ) ^ { 2 }$ is one-to-one if its domain is

A) $( - \infty , - 1 ]$
B) $( - \infty , \infty )$
C) $[ - 2 , \infty )$
D) $( - \infty , - 1 ) \cup ( - 1 , \infty )$
E) $( - \infty , 1 ]$

Question 68

The function $f ( x ) = ( 2 x - 1 ) ^ { 2 }$ is one-to-one if its domain is

A) $( - \infty , \infty )$
B) $\left( - \infty , \frac { 1 } { 2 } \right)$
C) $[ - 1 , \infty )$
D) $( - \infty , - 1 ) \cup ( 1 , \infty )$
E) $( - \infty , 2 ]$

Question 69

The function $f ( x ) = \frac { 2 } { x ^ { 2 } }$ is one-to-one if its domain is

A) $( - \infty , \infty )$
B) $( - \infty , 0 ) \cup ( 0 , \infty )$
C) $( 0 , \infty )$
D) $( - \infty , - 1 ) \cup ( 1 , \infty )$
E) $( - \infty , 1 ]$

Question 70

The function $f ( x ) = - x ^ { 2 }$ is one-to-one if its domain is

A) $( - \infty , \infty )$
B) $( - \infty , 0 ) \cup ( 0 , \infty )$
C) $( - \infty , 1 ]$
D) $[ 0 , \infty )$
E) $[ - 1 , \infty )$

Question 71

Consider the one-to-one function $f ( x ) = 2 ( x - 1 ) + 3$ . Then $f ^ { - 1 } ( x )$ is

A) $2 x - 1$
B) $\frac { x + 1 } { 2 }$
C) $\frac { 1 } { 2 x + 1 }$
D) $\frac { x - 1 } { 2 }$
E) $2 ( x + 1 ) + 3$

Question 72

Consider the one-to-one function $f ( x ) = 4 x ^ { 3 } - 5$ . Then $f ^ { - 1 } ( x )$ is

A) $4 x ^ { 3 } + 5$
B) $4 \sqrt [ 3 ] { x + 5 }$
C) $\frac { \sqrt [ 3 ] { x } } { 4 } - 5$
D) $\sqrt [ 3 ] { 4 }$
E) $\sqrt [ 3 ] { \frac { x + 5 } { 4 } }$

Question 73

Consider the one-to-one function $f ( x ) = \sqrt [ 3 ] { 2 x + 3 }$ . Then $f ^ { - 1 } ( x )$ is

A) $\left( \frac { x } { 2 } - 3 \right) ^ { 3 }$
B) $\left( \frac { x - 3 } { 2 } \right) ^ { 3 }$
C) $\frac { x ^ { 3 } - 3 } { 2 }$
D) $\left( \frac { x } { 2 } + 3 \right) ^ { 3 }$
E) $2 x ^ { 3 } - 3$

Question 74

Consider the one-to-one function $f ( x ) = \frac { 2 } { x }$ . Then $f ^ { - 1 } ( x )$ is

A) $- \frac { 2 } { x }$
B) $\frac { 2 } { x }$
C) $- \frac { x } { 2 }$
D) $\frac { x } { 2 }$
E) $\frac { 2 } { | x | }$

Question 75

Consider the one-to-one function $f ( x ) = \frac { 1 - x } { 1 + x }$ . Then $f ^ { - 1 } ( x )$ is

A) $\frac { 1 - x } { 1 + x }$
B) $\frac { x - 1 } { x + 1 }$
C) $\frac { 1 + x } { 1 - x }$
D) $\frac { 1 + x } { x - 1 }$
E) $\frac { 1 + \frac { 1 } { x } } { x - 1 }$

Question 76

Consider the one-to-one function $f ( x ) = \frac { 2 x - 1 } { 3 x + 4 }$ . Then $f ^ { - 1 } ( x )$ is

A) $\frac { 3 x + 4 } { 2 x - 1 }$
B) $\frac { 4 x + 3 } { 2 x - 1 }$
C) $\frac { 4 x + 3 } { 2 x + 1 }$
D) $\frac { 4 x - 3 } { 2 x + 1 }$
E) $\frac { 4 x + 1 } { 2 - 3 x }$

Question 77

Consider the one-to-one function $f ( x ) = \frac { 1 } { x - 2 }$ . Then $f ^ { - 1 } ( x )$ is

A) $x - 2$
B) $x + 2$
C) $\frac { 1 } { x + 2 }$
D) $\frac { 1 } { x } + 2$
E) $\frac { 2 } { x } + 1$

Question 78

Consider the one-to-one function $f ( x ) = \frac { 3 x } { 2 x - 1 }$ . Then $f ^ { - 1 } ( x )$ is

A) $\frac { 2 x - 1 } { 3 x }$
B) $\frac { 2 x + 1 } { 3 x }$
C) $\frac { x } { 3 x - 2 }$
D) $\frac { x } { 2 - 3 x }$
E) $\frac { x } { 2 x - 3 }$

Question 79

Consider the one-to-one function $f ( x ) = 2 - \sqrt [ 3 ] { x + 5 }$ . Then $f ^ { - 1 } ( x )$ is

A) $5 - ( 2 - x ) ^ { 3 }$
B) $5 + ( 2 - x ) ^ { 3 }$
C) $5 + ( x - 2 ) ^ { 3 }$
D) $( 2 - x ) ^ { 3 } - 5$
E) $( 2 + x ) ^ { 3 } - 5$

Question 80

Consider the one-to-one function $f ( x ) = 4 + \sqrt [ 3 ] { x - 7 }$ . Then $f ^ { - 1 } ( x )$ is

A) $( x + 7 ) ^ { 3 } - 4$
B) $( x - 4 ) ^ { 3 } - 7$
C) $( x - 7 ) ^ { 3 } + 4$
D) $( x + 4 ) ^ { 3 } - 7$
E) $( x - 4 ) ^ { 3 } + 7$