Deck 9: Exponential and Logarithmic Functions

Question 1

For the given functions f and g, find the composition.
$$f ( x ) = x ^ { 2 } + 3 x ; g ( x ) = \sqrt { x }$$
Find $( g \circ f ) ( 0 )$ .

A) 0
B) 3
C) $\sqrt { 3 }$
D) $2 \sqrt { 3 }$

Answer 1

A

Question 2

f(x)=x+7 ; g(x)=5x - 2
Find (f+g)(x) .

A) 5x+5
B) $5 x ^ { 2 } + 33 x - 14$
C) 11x
D) 6x+5

Answer 2

D

Question 3

$f ( x ) = 3 x ^ { 3 } - 1 ; g ( x ) = 3 x ^ { 2 } - 1$
Find $( f \cdot g ) ( x )$

A) $( f \cdot g ) ( x ) = 9 x ^ { 6 } - 3 x ^ { 3 } - 3 x ^ { 2 } + 1$
B) $( f \cdot g ) ( x ) = 3 x ^ { 3 } + 3 x ^ { 2 } + 1$
C) $( f \cdot g ) ( x ) = - 9 x ^ { 5 } - 3 x ^ { 3 } - 3 x ^ { 2 } + 1$
D) $( f \cdot g ) ( x ) = 9 x ^ { 5 } - 3 x ^ { 3 } - 3 x ^ { 2 } + 1$

Answer 3

D

Question 4

For the given functions f and g, find the composition.
$$f ( x ) = x ^ { 2 } + 2 x ; g ( x ) = x + 4$$
Find $( f \circ g ) ( 3 )$ .

A) $2 \sqrt { 3 }$
B) 0
C) 63
D) 19

Question 5

For the given functions f and g, find the composition.
$$f ( x ) = x ^ { 2 } + 6 x ; g ( x ) = x + 3$$
Find $( g \circ f ) ( 2 )$ .

A) 19
B) 21
C) 80
D) 55

Question 6

For the given functions f and g, find the composition.
$$f ( x ) = x ^ { 2 } + 9 x - 7 ; g ( x ) = \sqrt { x }$$
Find $( f \circ g ) ( 9 )$ .

A) 29
B) 36
C) 30
D) 23

Question 7

$f ( x ) = \sqrt { x } ; g ( x ) = 4 x - 1$
Find $\left( \frac { f } { g } \right) ( x )$

A) $\left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( \mathrm { x } ) = \frac { \sqrt { \mathrm { x } } } { 1 - 4 \mathrm { x } } , \text { where } x \neq \frac { 1 } { 4 }$
B) $\left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( \mathrm { x } ) = \frac { \sqrt { \mathrm { x } } } { 4 \mathrm { x } - 1 } , \text { where } x \neq \frac { 1 } { 4 }$
C) $\left( \frac { f } { g } \right) ( x ) = \frac { \sqrt { x } } { 4 x - 4 } , \text { where } x \neq 1$
D) $\left( \frac { f } { g } \right) ( x ) = \frac { 1 - 4 x } { \sqrt { x } } , \text { where } x \neq 0$

Question 8

$f ( x ) = \sqrt { x } ; g ( x ) = x + 9$
Find $( f + g ) ( x )$

A) $( f + g ) ( x ) = 9 \sqrt { x } + x$
B) $( f + g ) ( x ) = x \sqrt { x } + 9$
C) $( f + g ) ( x ) = \sqrt { x } + x + 9$
D) $( f + g ) ( x ) = x \sqrt { x } + x ^ { 2 } + 9 x$

Question 9

For the given functions f and g, find the composition.
$$f ( x ) = 6 x ^ { 2 } - 2 x ; g ( x ) = - 3 x$$
Find $( g \circ f ) ( x )$ .

A) $54 x ^ { 2 } - 2 x$
B) $6 x ^ { 2 } - 4$
C) $- 18 x ^ { 3 } + 6 x ^ { 2 }$
D) $- 18 x ^ { 2 } + 6 x$

Question 10

$f ( x ) = x + 2 ; g ( x ) = 8 x ^ { 2 }$
Find (f - g)(x)

A) $( f - g ) ( x ) = 8 x ^ { 2 } - x - 2$
B) $( f - g ) ( x ) = 8 x ^ { 2 } + x + 2$
C) $( f - g ) ( x ) = - 8 x ^ { 2 } + x + 2$
D) $( f - g ) ( x ) = - 8 x ^ { 2 } - x + 2$

Question 11

f(x)=8x - 7 ; g(x)=4x - 8
Find (f-g)(x) .

A) $( f - g ) ( x ) = 4 x + 1$
B) $( f - g ) ( x ) = 4 x - 15$
C) $( f - g ) ( x ) = - 4 x - 1$
D) $( f - g ) ( x ) = 12 x - 15$

Question 12

f(x) = 3x + 4; g(x)= 5x - 1
Find $\left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( \mathrm { x } ) .$

A) $\left( \frac { f } { g } \right) ( x ) = \frac { 3 x + 4 } { 5 x + 1 } , \text { where } x \neq - \frac { 1 } { 5 }$
B) $\left( \frac { f } { g } \right) ( x ) = \frac { 5 x + 1 } { 3 x + 4 } , \text { where } x \neq - \frac { 4 } { 3 }$
C) $\left( \frac { f } { g } \right) ( x ) = \frac { 5 x - 1 } { 3 x + 4 } , \text { where } x z - \frac { 4 } { 3 }$
D) $\left( \frac { f } { g } \right) ( x ) = \frac { 3 x + 4 } { 5 x - 1 } , \text { where } x \neq \frac { 1 } { 5 }$

Question 13

$f ( x ) = \sqrt { 3 x } ; g ( x ) = - 2 x + 7$
Find $( f \cdot g ) ( x )$

A) $( f \cdot g ) ( x ) = \sqrt { 3 x } + 14 x$
B) $( f \cdot g ) ( x ) = - 2 x \sqrt { 3 x } + 7 \sqrt { 3 x }$
C) $( f \cdot g ) ( x ) = - 6 x + 7 \sqrt { 3 x }$
D) $( f \cdot g ) ( x ) = - 6 x ^ { 2 } + 21$

Question 14

For the given functions f and g, find the composition.
$$f ( x ) = \sqrt { x + 3 } ; g ( x ) = 2 x$$
Find $( f \circ g ) ( 2 )$ .

A) $2 \sqrt { 5 }$
B) $\sqrt { 7 }$
C) $\sqrt { 10 }$
D) $2 \sqrt { 10 }$

Question 15

$f ( x ) = 3 x ^ { 8 } ; g ( x ) = 8 x ^ { 7 }$
Find $( f \cdot g ) ( x )$

A) $( f \cdot g ) ( x ) = 24 x ^ { 56 }$
B) $( f \cdot g ) ( x ) = 24 x ^{15}$
C) $( f \cdot g ) ( x ) = - 24 x ^ { 15 }$
D) $( f \cdot g ) ( x ) = - 24 x ^ { 56 }$

Question 16

Solve.
Business people are concerned with cost functions, revenue functions, and profit functions. Suppose the revenue $R ( x )$ for $x$ units of a product can be described by $R ( x ) = 410 x$ , and the cost $C ( x )$ can be described by $C ( x )$ $= 2900 + 110 x$ . Find the profit $P ( x )$ for $x$ units.

A) $P ( x ) = \frac { 300 } { x } - 2900$
B) $\mathrm { P } ( \mathrm { x } ) = 300 \mathrm { x } + 2900$
C) $P ( x ) = 300 x - 2900$
D) $P ( x ) = 520 x - 2900$

Question 17

For the given functions f and g, find the composition.
$$f ( x ) = 6 x ^ { 2 } + 5 x ; g ( x ) = 2 x$$
Find $( f \circ g ) ( x )$ .

A) $24 x ^ { 2 } + 10 x$
B) $6 x ^ { 2 } + 7$
C) $12 x ^ { 2 } + 10 x$
D) $12 x ^ { 3 } + 10 x ^ { 2 }$

Question 18

$f ( x ) = \sqrt [ 3 ] { x } ; g ( x ) = 3 x - 6$
Find $( f - g ) ( x )$

A) $( f - g ) ( x ) = \sqrt [ 3 ] { x } - 3 x + 6$
B) $( f - g ) ( x ) = \sqrt [ 3 ] { x } - 3 x - 6$
C) $( f - g ) ( x ) = \sqrt [ 3 ] { x } + 3 x + 6$
D) $( f - g ) ( x ) = - \sqrt [ 3 ] { x } - 3 x + 6$

Question 19

f(x)=4 x-1 ; g(x)=6 x-2
Find $( f \cdot g ) ( x )$

A) $( f \cdot g ) ( x ) = 24 x ^ { 2 } - 8 x + 2$
B) $( f \cdot g ) ( x ) = 10 x ^ { 2 } - 14 x - 3$
C) $( f \cdot g ) ( x ) = 24 x ^ { 2 } + 2$
D) $( f \cdot g ) ( x ) = 24 x ^ { 2 } - 14 x + 2$

Question 20

$f ( x ) = - 4 x ^ { 4 } ; g ( x ) = - 2 x ^ { 2 }$
Find $\left( \frac { f } { g } \right) ( x ) .$

A) $\left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( \mathrm { x } ) = 8 \mathrm { x } ^ { 6 } , \text { where } \mathrm { x } \neq 0$
B) $\left( \frac { f } { g } \right) ( x ) = 2 x ^ { 2 } , \text { where } x \neq 0$
C) $\left( \frac { f } { g } \right) ( x ) = - 2 x ^ { 2 } , \text { where } x \neq 0$
D) $\left( \frac { f } { g } \right) ( x ) = 2 x ^ { 4 } , \text { where } x \neq 0$

Question 21

Write the function F(x) as a composition of f, g, or h.
$$\begin{array} { l } f ( x ) = x ^ { 2 } + 6 \quad g ( x ) = - 2 x \quad h ( x ) = \sqrt { x - 4 } \\F ( x ) = \sqrt { - 2 x - 4 }\end{array}$$

A) $\mathrm { F } ( \mathrm { x } ) = ( \mathrm { h } \circ \mathrm { g } ) ( \mathrm { x } )$
B) $\mathrm { F } ( \mathrm { x } ) = ( \mathrm { h } \circ \mathrm { f } ) ( \mathrm { x } )$
C) $F ( x ) = ( g \circ h ) ( x )$
D) $F ( x ) = ( f \circ h ) ( x )$

Question 22

Write the function F(x) as a composition of f, g, or h.
$$\begin{array} { l } f ( x ) = x ^ { 2 } - 3 \quad g ( x ) = 3 x \quad h ( x ) = \sqrt { x - 1 } \\F ( x ) = x - 4\end{array}$$

A) $F ( x ) = ( g \circ h ) ( x )$
B) $\mathrm { F } ( \mathrm { x } ) = ( \mathrm { h } \circ \mathrm { g } ) ( \mathrm { x } )$
C) $F ( x ) = ( f \circ g ) ( x )$
D) $F ( x ) = ( f \circ h ) ( x )$

Question 23

Determine whether the function is a one-to-one function.
$$f = \{ ( 3,1 ) , ( - 3 , - 1 ) , ( - 5,1 ) , ( 5 , - 1 ) \}$$

A) one-to-one
B) not one-to-one

Question 24

Write the function F(x) as a composition of f, g, or h.
$$\begin{array} { l } f ( x ) = x ^ { 2 } + 6 \quad g ( x ) = 7 x \quad h ( x ) = \sqrt { x + 3 } \\F ( x ) = \sqrt { 7 x + 3 }\end{array}$$

A) $\mathrm { F } ( \mathrm { x } ) = ( \mathrm { h } \circ \mathrm { g } ) ( \mathrm { x } )$
B) $\mathrm { F } ( \mathrm { x } ) = ( \mathrm { h } \circ \mathrm { f } ( \mathrm { x } )$
C) $\mathrm { F } ( \mathrm { x } ) = ( \mathrm { g } \circ \mathrm { h } ) ( \mathrm { x } )$
D) $\mathrm { F } ( \mathrm { x } ) = ( \mathrm { f } \circ \mathrm { h } ) ( \mathrm { x } )$

Question 25

Determine whether the function is a one-to-one function.
$$\mathrm { f } = \{ ( - 3,17 ) , ( - 4 , - 5 ) , ( - 18,19 ) \}$$

A) one-to-one
B) not one-to-one

Question 26

Write the function F(x) as a composition of f, g, or h.
$$\begin{array} { l } f ( x ) = x ^ { 2 } - 2 \quad g ( x ) = 3 x \quad h ( x ) = \sqrt { x - 8 } \\F ( x ) = 3 x ^ { 2 } - 6\end{array}$$

A) $F ( x ) = ( f \circ g ) ( x )$
B) $F ( x ) = ( g \circ h ) ( x )$
C) $\mathrm { F } ( \mathrm { x } ) = ( \mathrm { h } \circ \mathrm { g } ) ( \mathrm { x } )$
D) $F ( x ) = ( g \circ f ) ( x )$

Question 27

Find f(x) and g(x) so that the given function h(x) = (f ° g)(x).
$$h ( x ) = \sqrt [ 3 ] { x + 4 }$$

A) $f ( x ) = \sqrt [ 3 ] { x } ; g ( x ) = x + 4$
B) $f ( x ) = x ^ { 3 } ; g ( x ) = x + 4$
C) $f ( x ) = \sqrt { x } ; g ( x ) = x + 4$
D) $f ( x ) = x + 4 ; g ( x ) = \sqrt [ 3 ] { x }$

Question 28

For the given functions f and g, find the composition.
$$f ( x ) = \sqrt { x + 8 } ; g ( x ) = 8 x - 12$$
Find $( g \circ f ) ( x )$ .

A) $8 \sqrt { x + 8 } - 12$
B) $2 \sqrt { 2 x - 1 }$
C) $2 \sqrt { 2 x + 1 }$
D) $8 \sqrt { x - 4 }$

Question 29

Find f(x) and g(x) so that the given function h(x) = (f ° g)(x).
$$h ( x ) = \frac { 1 } { x + 5 }$$

A) $f ( x ) = \frac { 1 } { x - 1 } ; g ( x ) = x + 5$
B) $f ( x ) = x + 5 ; g ( x ) = \frac { 1 } { x }$
C) $f ( x ) = \frac { 5 } { x } ; g ( x ) = x - 1$
D) $f ( x ) = \frac { 1 } { x } ; g ( x ) = x + 5$

Question 30

For the given functions f and g, find the composition.
$$f ( x ) = - 2 x + 5 ; g ( x ) = 5 x + 9$$
Find $( g \circ f ) ( x )$ .

A) $10 x + 34$
B) $- 10 x + 34$
C) $- 10 x + 23$
D) $- 10 x - 16$

Question 31

Write the function F(x) as a composition of f, g, or h.
$$\begin{array} { l } f ( x ) = x ^ { 2 } - 4 \quad g ( x ) = 5 x \quad h ( x ) = \sqrt { x - 4 } \\F ( x ) = 25 x ^ { 2 } - 4\end{array}$$

A) $F ( x ) = ( g \circ h ) ( x )$
B) $F ( x ) = ( g \circ f ) ( x )$
C) $F ( x ) = ( h \circ g ) ( x )$
D) $F ( x ) = ( f \circ g ) ( x )$

Question 32

For the given functions f and g, find the composition.
$$f ( x ) = \sqrt { x + 3 } ; g ( x ) = 8 x - 7$$
Find $( f \circ g ) ( x )$ .

A) $8 \sqrt { x - 4 }$
B) $2 \sqrt { 2 x - 1 }$
C) $2 \sqrt { 2 x + 1 }$
D) $8 \sqrt { x + 3 } - 7$

Question 33

Determine whether the function is a one-to-one function.
$$\mathrm { f } = \{ ( - 7 , - 8 ) , ( 8,7 ) , ( 1,1 ) , ( - 1 , - 1 ) \}$$

A) one-to-one
B) not one-to-one

Question 34

For the given functions f and g, find the composition.
$$f ( x ) = 4 x + 5 ; g ( x ) = 5 x - 1$$
Find $( f \circ g ) ( x )$ .

A) $20 x + 24$
B) $20 x + 9$
C) $20 x + 4$
D) $20 x + 1$

Question 35

Find f(x) and g(x) so that the given function h(x) = (f ° g)(x).
$$h ( x ) = \left( 9 - 8 x ^ { 3 } \right) ^ { 2 }$$

A) $f ( x ) = 9 - 8 x ^ { 3 } ; g ( x ) = x ^ { 2 }$
B) $f ( x ) = x ^ { 2 } ; g ( x ) = 9 - 8 x$
C) $f ( x ) = x ^ { 2 } ; g ( x ) = 9 - 8 x ^ { 3 }$
D) $f ( x ) = 9 - 8 x ^ { 2 } ; g ( x ) = x ^ { 3 }$

Question 36

Determine whether the function is a one-to-one function.
$$f = \{ ( 6 , - 5 ) , ( - 4 , - 4 ) , ( - 6 , - 3 ) , ( - 8 , - 2 ) \}$$

A) one-to-one
B) not one-to-one

Question 37

For the given functions f and g, find the composition.
$$f ( x ) = x ^ { 3 } + 6 x ; g ( x ) = - 3 x$$
Find $( f \circ g ) ( x )$ .

A) $- 27 x ^ { 3 } - 18 x$
B) $- 27 x ^ { 2 } - 18 x$
C) $- 3 x ^ { 3 } + 6 x$
D) $- 3 x ^ { 3 } - 18 x$

Question 38

For the given functions f and g, find the composition.
$$f ( x ) = x ^ { 3 } - 5 x ; g ( x ) = - 3 x$$
Find $( g \circ f ) ( x )$ .

A) $- 27 x ^ { 2 } + 15 x$
B) $- 27 x ^ { 3 } + 15 x$
C) $- 3 x ^ { 3 } + 15 x$
D) $- 3 x ^ { 3 } - 5 x$

Question 39

Find f(x) and g(x) so that the given function h(x) = (f ° g)(x).
$$h ( x ) = \left| 6 - 7 x ^ { 2 } \right|$$

A) $f ( x ) = | x | ; g ( x ) = 6 - 7 x$
B) $f ( x ) = 6 - 7 x ^ { 2 } ; g ( x ) = | x |$
C) $f ( x ) = 6 - 7 x ^ { 2 } ; g ( x ) = \left| x ^ { 2 } \right|$
D) $f ( x ) = | x | ; g ( x ) = 6 - 7 x ^ { 2 }$

Question 40

Write the function F(x) as a composition of f, g, or h.
$$\begin{array} { l } f ( x ) = x ^ { 2 } - 1 \quad g ( x ) = - 4 x \quad h ( x ) = \sqrt { x - 2 } \\F ( x ) = \sqrt { x ^ { 2 } - 3 }\end{array}$$

A) $\mathrm { F } ( \mathrm { x } ) = ( \mathrm { h } \circ \mathrm { f } ) ( \mathrm { x } )$
B) $F ( x ) = ( h \circ g ) ( x )$
C) $\mathrm { F } ( \mathrm { x } ) = ( \mathrm { g } \circ \mathrm { h } ) ( \mathrm { x } )$
D) $F ( x ) = ( f \circ h ) ( x )$

Question 41

If the function is one-to-one, list the inverse function by switching coordinates or inputs and outputs.
f = {(-6, -9), (6, 9), (7, 11), (-7, -11)}

A) f-1 = {(-9, -6), (9, 6), (11, 6), (-11, -7)}
B) f-1 = {(-9, -6), (-6, 6), (11, 7), (-11, -7)}
C) f-1 = {(-9, -6), (9, 6), (11, 7), (-11, -7)}
D) not one-to-one

Question 42

Determine whether the function is a one-to-one function.
$$f = \{ ( - 3,2 ) , ( - 2,2 ) , ( - 1,1 ) , ( 0 , - 8 ) \}$$

A) one-to-one
B) not one-to-one

Question 43

Determine whether the function is a one-to-one function.
$\begin{array}{l|c|c|c|c|c|c}\text { Month of } 1999 \text { (input) } & \text { Jan } & \text { Feb } & \text { Mar } & \text { Apr } & \text { May } & \text { Jun } \\\hline \begin{array}{l}\text { Sales of Product B } \\\text { (output) }\end{array} & 3410 & 3863 & 3108 & 3712 & 4014 & 3863\end{array}$

A) one-to-one
B) not one-to-one

Question 44

Determine whether the graph of the function is the graph of a one-to-one function.

A) Yes
B) No

Question 45

If the function is one-to-one, list the inverse function by switching coordinates or inputs and outputs.
$$\mathrm { f } = \{ ( - 5,1 ) , ( - 1,5 ) , ( - 7 , - 7 ) , ( 7,7 ) \}$$

A) $f ^ { - 1 } = \{ ( 7 , - 7 ) , ( - 7 , - 1 ) , ( 1 , - 5 ) , ( - 7,7 ) \}$
B) $\mathrm { f } ^ { - 1 } = \{ ( 1 , - 5 ) , ( 5 , - 1 ) , ( - 7 , - 7 ) , ( 7,7 ) \}$
C) $f ^ { - 1 } = \{ ( 7 , - 7 ) , ( 5 , - 1 ) , ( 1 , - 1 ) , ( - 7,7 ) \}$
D) not one-to-one

Question 46

Determine whether the graph of the function is the graph of a one-to-one function.

A) Yes
B) No

Question 47

If the function is one-to-one, list the inverse function by switching coordinates or inputs and outputs.

Question 48

If the function is one-to-one, list the inverse function by switching coordinates or inputs and outputs.
$$f = \{ ( 9 , - 5 ) , ( 4,17 ) , ( - 18,11 ) \}$$

A) $f ^ { - 1 } = \{ ( - 5,9 ) , ( 17,4 ) , ( 11 , - 18 ) \}$
B) $\mathrm { f } ^ { - 1 } = \{ ( - 5,9 ) , ( - 18,4 ) , ( 11,17 ) \}$
C) $\mathrm { f } ^ { - 1 } = \{ ( 9,17 ) , ( 9,4 ) , ( 11 , - 18 ) \}$
D) not one-to-one

Question 49

Determine whether the graph of the function is the graph of a one-to-one function.

A) Yes
B) No

Question 50

Determine whether the function is a one-to-one function.
$\begin{array}{l|c|c|c|c|c}\text { Weekdays (input) } & \text { Monday } & \text { Tuesday } & \text { Wednesday } & \text { Thursday } & \text { Friday } \\\hline \text { Student: Avg. } & & & & & \\\text { Minutes of Study(outputt) } 249 & 324 & 410 & 123 & 144\end{array}$

A) one-to-one
B) not one-to-one

Question 51

Determine whether the graph of the function is the graph of a one-to-one function.

A) Yes
B) No

Question 52

Determine whether the graph of the function is the graph of a one-to-one function.

A) Yes
B) No

Question 53

For the given one-to-one function f, find the following.
$$f ( x ) = \sqrt { 6 x - 5 } - 5$$
Find $f ( 5 )$ and $f ^ { - 1 } ( 0 )$ .

A) $f ( 5 ) = 25 ; f ^ { - 1 } ( 0 ) = 5$
B) $\mathrm { f } ( 5 ) = \frac { 25 } { 6 } ; \mathrm { f } ^ { - 1 } ( 0 ) = 0$
C) $\mathrm { f } ( 5 ) = 0 ; \mathrm { f } ^ { - 1 } ( 0 ) = 5$
D) $f ( 5 ) = 5 ; f ^ { - 1 } ( 0 ) = 0$

Question 54

For the given one-to-one function f, find the following.
$$f ( x ) = x ^ { 3 } + 9$$
Find $f ( - 1 )$ and $f ^ { - 1 } ( 8 )$ .

A) $f ( - 1 ) = - 10 ; f ^ { - 1 } ( 8 ) = - 1$
B) $f ( - 1 ) = 8 ; f ^ { - 1 } ( 8 ) = \frac { 1 } { 8 }$
C) $f ( - 1 ) = 8 ; f ^ { - 1 } ( 8 ) = - 1$
D) $f ( - 1 ) = - 1 ; f ^ { - 1 } ( 8 ) = 8$

Question 55

If the function is one-to-one, list the inverse function by switching coordinates or inputs and outputs.
$$f = \{ ( 6 , - 2 ) , ( 9 , - 1 ) , ( 7,0 ) , ( 5,1 ) \}$$

A) $\mathrm { f } ^ { - 1 } = \{ ( - 1 , - 2 ) , ( - 2,7 ) , ( 6,9 ) , ( - 1,0 ) \}$
B) $\mathrm { f } ^ { - 1 } = \{ ( - 1 , - 2 ) , ( 1,7 ) , ( 6,7 ) , ( - 1,0 ) \}$
C) $\mathrm { f } ^ { - 1 } = \{ ( - 2,6 ) , ( - 1,9 ) , ( 0,7 ) , ( 1,5 ) \}$
D) not one-to-one

Question 56

Determine whether the graph of the function is the graph of a one-to-one function.

A) Yes
B) No

Question 57

Determine whether the graph of the function is the graph of a one-to-one function.

A) Yes
B) No

Question 58

Determine whether the function is a one-to-one function.
$$f = \{ ( - 8 , - 6 ) , ( - 18 , - 6 ) , ( - 5,8 ) \}$$

A) one-to-one
B) not one-to-one

Question 59

If the function is one-to-one, list the inverse function by switching coordinates or inputs and outputs.

Question 60

Determine whether the graph of the function is the graph of a one-to-one function.

A) Yes
B) No

Question 61

Determine whether the functions f and g are inverses of each other.
$$f ( x ) = x ^ { 3 } + 8 ; g ( x ) = \sqrt [ 3 ] { x - 8 }$$

A) Yes
B) $\mathrm { No }$

Question 62

Find the inverse of the one-to-one function.
$f ( x ) = \sqrt [ 3 ] { x - 8 }$

A) $f ^ { - 1 } ( x ) = \frac { 1 } { x ^ { 3 } + 8 }$
B) $f ^ { - 1 } ( x ) = x ^ { 3 } + 64$
C) $f ^ { - 1 } ( x ) = x + 8$
D) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \mathrm { x } ^ { 3 } + 8$

Question 63

Graph the function and its inverse on the same set of axes.
$$f ( x ) = x ^ { 3 } + 2$$

A)

B)

C)

D)

Question 64

Determine whether the functions f and g are inverses of each other.
$$f ( x ) = 3 x + 2 ; g ( x ) = \frac { x + 2 } { 3 }$$

A) $Y e s$
B) $\mathrm { No }$

Question 65

Graph the inverse of the function on the same set of axes.

A)

B)

C)

D)

Question 66

Find the inverse of the one-to-one function.
$$f ( x ) = ( x + 7 ) ^ { 3 } - 3$$

A) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt [ 3 ] { \mathrm { x } + 3 } - 7$
B) $f ^ { - 1 } ( x ) = - \sqrt [ 3 ] { x + 3 } + 7$
C) $f ^ { - 1 } ( x ) = \sqrt [ 3 ] { x + 3 } + 7$
D) $f ( x ) = ( x + 3 ) ^ { 3 } - 7$

Question 67

Determine whether the functions f and g are inverses of each other.
$$f ( x ) = ( x + 4 ) ^ { 3 } + 1 ; g ( x ) = \sqrt [ 3 ] { x - 1 } - 4$$

A) $Y e s$
B) $\mathrm { No }$

Question 68

Determine whether the functions f and g are inverses of each other.
$$f ( x ) = 4 x + 5 ; g ( x ) = \frac { x - 5 } { 4 }$$

A) Yes
B) $\mathrm { No }$

Question 69

Graph the function and its inverse on the same set of axes.
$$f ( x ) = \frac { 1 } { 2 } x - 2$$

A)

B)

C)

D)

Question 70

Graph the inverse of the function on the same set of axes.

A)

B)

C)

D)

Question 71

Find the inverse of the one-to-one function.
$$f ( x ) = 5 x + 7$$

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

Question 72

Graph the inverse of the function on the same set of axes.

A)

B)

C)

D)

Question 73

Find the inverse of the one-to-one function.
$$f ( x ) = \frac { 8 x + 5 } { 7 }$$

A) $f ^ { - 1 } ( x ) = \frac { 7 } { 8 x + 5 }$
B) $f ^ { - 1 } ( x ) = \frac { 7 x - 5 } { 8 }$
C) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 7 \mathrm { x } + 5 } { 8 }$
D) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 7 } { 8 x - 5 }$

Question 74

Graph the function and its inverse on the same set of axes.
$f(x)=4 x$

A)

B)

C)

D)

Question 75

Graph the function and its inverse on the same set of axes.
$$f ( x ) = - 2 x + 1$$

A)


B)

C)

D)

Question 76

Find the inverse of the one-to-one function.
$$f ( x ) = x ^ { 3 } + 2$$

A) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt [ 3 ] { \mathrm { x } + 2 }$
B) $f ^ { - 1 } ( x ) = \sqrt [ 3 ] { x - 2 }$
C) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt [ 3 ] { \mathrm { x } } - 2$
D) $f ^ { - 1 } ( x ) = - x ^ { 3 } - 2$

Question 77

Determine whether the functions f and g are inverses of each other.
$$f ( x ) = x ^ { 3 } + 8 ; g ( x ) = \sqrt [ 3 ] { x } - 8$$

A) Yes
B) No

Question 78

Graph the inverse of the function on the same set of axes.

A)

B)

C)

D)

Question 79

Graph the inverse of the function on the same set of axes.

A)

B)

C)

D)

Question 80

Find the inverse of the one-to-one function.
$$f ( x ) = \frac { 5 } { 6 x - 7 }$$

A) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 6 \mathrm { x } - 7 } { 5 }$
B) $f ^ { - 1 } ( x ) = \frac { 5 } { 6 x } + \frac { 7 } { 6 }$
C) $f ^ { - 1 } ( x ) = \frac { 5 } { 6 y } + \frac { 7 } { 6 }$
D) $f ^ { - 1 } ( x ) = - \frac { 7 } { 6 } - \frac { 5 } { 6 x }$