Deck 4: Exponential and Logarithmic Functions

Question 1

Evaluate the expression using the graphs of y = f(x) and y = g(x).
Evaluate (fg)(-1).

A) 0
B) -2
C) 3
D) -1

Answer 1

B

Question 2

Evaluate the expression using the values given in the table.

- $$\begin{array}{l}( g f ) ( 1 )\\\begin{array} { c | r | r | r | r } x & 1 & 6 & 10 & 12 \\\hline f ( x ) & - 2 & 10 & 3 & 12\end{array}\\\begin{array} { c | r | r | r | r } \mathrm { x } & - 5 & - 2 & 1 & 3 \\\hline \mathrm { g } ( \mathrm { x } ) & 1 & - 5 & 6 & 10\end{array}\end{array}$$

A) 10
B) -2
C) 6
D) -5

Answer 2

-5

Question 3

For the given functions f and g, find the requested composite function value.

- $f ( x ) = 4 x + 6 , \quad g ( x ) = 4 x ^ { 2 } + 3 ; \quad$ Find $( g \circ f ) ( 3 )$

A) 6,087
B) 78
C) 162
D) 1,299

Answer 3

1,299

Question 4

For the given functions f and g, find the requested composite function.

- $f ( x ) = \frac { 5 } { x - 1 } , \quad g ( x ) = \frac { 1 } { 6 x } ; \quad$ Find $( f \circ g ) ( x )$

A) $\frac { 5 x } { 1 - 6 x }$

B) $\frac { 1 \mathrm { x } - 1 } { 30 \mathrm { x } }$

C) $\frac { 30 x } { 1 + 6 x }$

D) $\frac { 30 x } { 1 - 6 x }$

Question 5

For the given functions f and g, find the requested composite function.

- $$f ( x ) = \frac { 7 } { x - 3 } , g ( x ) = \frac { 2 } { 5 x } ; \quad \text { Find } ( f \circ g ) ( x )$$

A) $\frac { 35 x } { 2 - 15 x }$

B) $\frac { 7 x } { 2 - 15 x }$

C) $\frac { 2 x - 6 } { 35 x }$

D) $\frac { 35 x } { 2 + 15 x }$

Question 6

For the given functions f and g, find the requested composite function.

- $$f ( x ) = \frac { x - 10 } { 2 } , \quad g ( x ) = 2 x + 10 ; \quad \text { Find } ( g \circ f ) ( x )$$

A) x
B) 2x + 10
C) x - 5
D) x + 20

Question 7

For the given functions f and g, find the requested composite function value.

- $$f ( t ) = \sqrt { t 4 + 18 t ^ { 2 } + 81 } , \quad g ( t ) = \frac { t + 3 } { 3 } ; \quad \text { Find } ( f \circ g ) ( 9 )$$

A) 25
B) 360
C) 31
D) 625

Question 8

For the given functions f and g, find the requested composite function value.

- $$f ( x ) = 2 x + 2 , \quad g ( x ) = 2 x ^ { 2 } + 1 ; \quad \text { Find } ( f \circ f ) ( 0 )$$

A) 4
B) 3
C) 9
D) 6

Question 9

For the given functions f and g, find the requested composite function value.

- $$f ( x ) = 2 x + 2 , \quad g ( x ) = 2 x ^ { 2 } + 3 ; \quad \text { Find } ( f \circ f ) ( 0 )$$

A) 21
B) 8
C) 6
D) 11

Question 10

For the given functions f and g, find the requested composite function value.

- $f ( x ) = \sqrt { x + 2 } , \quad g ( x ) = 3 x ; \quad$ Find $( f \circ g ) ( 0 )$ .

A) $3 \sqrt { 6 }$
B) $3 \sqrt { 2 }$
C) $\sqrt { 6 }$
D) $\sqrt { 2 }$

Question 11

For the given functions f and g, find the requested composite function.

- $f ( x ) = \sqrt { x + 2 } , \quad g ( x ) = 8 x - 6 ; \quad$ Find $( f \circ g ) ( x )$

A) $8 \sqrt { x - 4 }$
B) $2 \sqrt { 2 x - 1 }$
C) $8 \sqrt { x + 2 } - 6$
D) $2 \sqrt { 2 x + 1 }$

Question 12

For the given functions f and g, find the requested composite function.
f(x) = -2x + 3, g(x) = 6x + 4; Find (g °f)(x).

A) -12x + 22
B) -12x + 11
C) -12x - 14
D) 12x + 22

Question 13

For the given functions f and g, find the requested composite function value.

- $f ( x ) = 13 x ^ { 2 } - 4 x , \quad g ( x ) = 16 x - 10 ; \quad$ Find $( f \circ g ) ( 9 )$ .

A) 16,262
B) 136,278
C) 232,892
D) 216,630

Question 14

For the given functions f and g, find the requested composite function.

- $f ( x ) = 4 x ^ { 2 } + 6 x + 3 , \quad g ( x ) = 6 x - 7 ; \quad$ Find $( g \circ f ) ( x )$

A) $4 x ^ { 2 } + 36 x + 11$
B) $24 x ^ { 2 } + 36 x + 25$
C) $4 x ^ { 2 } + 6 x - 4$
D) $24 x ^ { 2 } + 36 x + 11$

Question 15

Evaluate the expression using the values given in the table.

- $$\begin{array}{l}( \mathrm { f } \mathrm { g } ) ( 3 )\\\begin{array} { c | r | r | r | r } \mathrm { x } & 1 & 7 & 10 & 12 \\\hline \mathrm { f } ( \mathrm { x } ) & - 2 & 10 & 0 & 12\end{array}\\\begin{array} { c | r | r | r | r } x & - 5 & - 2 & 1 & 3 \\\hline g ( x ) & 1 & - 7 & 7 & 10\end{array}\end{array}$$

A) Undefined
B) 10
C) 7
D) 0

Question 16

For the given functions f and g, find the requested composite function.
f(x) = 5x + 10, g(x) = 5x - 1; Find (f °g)(x).

A) 25x + 9
B) 25x + 15
C) 25x + 49
D) 25x + 5

Question 17

For the given functions f and g, find the requested composite function.

- $f ( x ) = \frac { x - 2 } { 3 } , g ( x ) = 3 x + 2 ; \quad$ Find $( g \circ f ) ( x )$

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

Question 18

For the given functions f and g, find the requested composite function value.

- $f ( x ) = 5 x + 8 , \quad g ( x ) = - 1 / x ; \quad$ Find $( g \circ f ) ( 3 )$ .

A) $- \frac { 1 } { 23 }$
B) $\frac { 19 } { 3 }$
C) $\frac { 68 } { 3 }$
D) $- \frac { 23 } { 3 }$

Question 19

For the given functions f and g, find the requested composite function value.

- $f ( x ) = \left| 20 x ^ { 2 } - 4 x \right| , \quad g ( x ) = 12 x - 4 ; \quad$ Find $( f \circ g ) ( 4 )$

A) 34,900
B) 38,544
C) 3,644
D) 13,376

Question 20

For the given functions f and g, find the requested composite function value.

- $f ( x ) = \frac { x - 6 } { x } , g ( x ) = x ^ { 2 } + 9 ; \quad$ Find $( g \circ f ) ( - 2 )$

A) $\frac { 7 } { 13 }$
B) 13
C) $\frac { 145 } { 16 }$
D) 25

Question 21

Find functions f and g so that f $f \circ g = H$

- $$H ( x ) = \frac { 6 } { \sqrt { 9 x + 10 } }$$

A) $f ( x ) = 6 ; \quad g ( x ) = \sqrt { 9 + 10 }$
B) $f ( x ) = \frac { 6 } { x } ; \quad g ( x ) = 9 x + 10$
C) $f ( x ) = \frac { 6 } { \sqrt { x } } ; \quad g ( x ) = 9 x + 10$
D) $f ( x ) = \sqrt { 9 x + 10 } ; g ( x ) = 6$

Question 22

Decide whether the composite functions, f $$f \circ g$$ nd $\mathbf { g } \circ \mathrm { f }$ f, are equal to x.

- $f ( x ) = \frac { 1 } { x } , g ( x ) = x$

A) Yes, no
B) No, no
C) Yes, yes
D) No, yes

Question 23

Solve the problem.

-An oil well off the Gulf Coast is leaking, with the leak spreading oil over the surface of the gulf as a circle. At any time t, in minutes, after the beginning of the leak, the radius of the oil slick on the surface is r(t) = 3t ft. Find
The area A of the oil slick as a function of time.

A) $\mathrm { A } ( \mathrm { r } ( \mathrm { t } ) ) = 9 \pi \mathrm { t } ^ { 2 }$
B) $A ( r ( t ) ) = 9 t ^ { 2 }$
C) $\mathrm { A } ( \mathrm { r } ( \mathrm { t } ) ) = 9 \pi \mathrm { t }$
D) $\mathrm { A } ( \mathrm { r } ( \mathrm { t } ) ) = 3 \pi \mathrm { t } ^ { 2 }$

Question 24

Find functions f and g so that f $f \circ g = H$

- $$\mathrm { H } ( \mathrm { x } ) = \sqrt { \frac { 1 } { \mathrm { x } - 2 } }$$

A) $g ( x ) = \sqrt { x } ; f ( x ) = \frac { 1 } { x - 2 }$

B) $f ( x ) = x - 2 ; g ( x ) = \frac { 1 } { \sqrt { x } }$

C) $f ( x ) = \frac { 1 } { x - 2 } ; g ( x ) = \sqrt { x }$

D) $f ( x ) = \frac { 1 } { x - 2 } ; g ( x ) = \frac { 1 } { \sqrt { x } }$

Question 25

Decide whether the composite functions, f $$f \circ g$$ nd $\mathbf { g } \circ \mathrm { f }$ f, are equal to x.

- $f ( x ) = x ^ { 2 } + 1 , g ( x ) = \sqrt { x } - 1$

A) No, yes
B) No, no
C) Yes, yes
D) Yes, no

Question 26

Decide whether the composite functions, f $$f \circ g$$ nd $\mathbf { g } \circ \mathrm { f }$ f, are equal to x.

- $f ( x ) = \frac { x - 6 } { 4 } , \quad g ( x ) = 4 x + 6$

A) Yes, yes
B) No, yes
C) No, no
D) Yes, no

Question 27

Decide whether the composite functions, f $$f \circ g$$ nd $\mathbf { g } \circ \mathrm { f }$ f, are equal to x.

- $f ( x ) = \sqrt { x + 1 } , g ( x ) = x ^ { 2 }$

A) Yes, yes
B) No, yes
C) Yes, no
D) No, no

Question 28

Find functions f and g so that f $f \circ g = H$

- $$H ( x ) = \left| 4 - 3 x ^ { 2 } \right|$$

A) $f ( x ) = 4 - 3 x ^ { 2 } ; g ( x ) = | x |$
B) $f ( x ) = x ^ { 2 } ; g ( x ) = 4 - 3 | x |$
C) $f ( x ) = 4 - 3 | x | ; g ( x ) = x ^ { 2 }$
D) $f ( x ) = | x | ; g ( x ) = 4 - 3 x ^ { 2 }$

Question 29

For the given functions f and g, find the requested composite function.

- $f ( x ) = x ^ { 2 } - 5 , \quad g ( x ) = x ^ { 2 } - 8 ; \quad$ Find $( f \circ g ) ( x )$

A) $x ^ { 4 } - 16 x ^ { 2 } + 59$
B) $x ^ { 4 } + 17$
C) $x ^ { 4 } + 59$
D) $x ^ { 4 } - 10 x ^ { 2 } + 17$

Question 30

Find functions f and g so that f $f \circ g = H$

- $$H ( x ) = \frac { 1 } { x ^ { 2 } - 5 }$$

A) $f ( x ) = \frac { 1 } { x ^ { 2 } } ; \quad g ( x ) = - 1 / 5$
B) $f ( x ) = \frac { 1 } { x } ; \quad g ( x ) = x ^ { 2 } - 5$
C) $f ( x ) = x ^ { 2 } - 5 ; \quad g ( x ) = \frac { 1 } { x }$
D) $f ( x ) = \frac { 1 } { x ^ { 2 } } ; \quad g ( x ) = x - 5$

Question 31

Find functions f and g so that f $f \circ g = H$

- $$H ( x ) = \frac { 1 } { x ^ { 2 } - 6 }$$

A) $f ( x ) = \frac { 1 } { x } ; g ( x ) = \frac { 1 } { x ^ { 2 } } - 9$
B) $f ( x ) = \frac { 1 } { x ^ { 2 } } - 9 ; g ( x ) = \frac { 1 } { x }$
C) $f ( x ) = x ^ { 2 } - 6 ; g ( x ) = \frac { 1 } { x }$
D) $f ( x ) = \frac { 1 } { x } , g ( x ) = x ^ { 2 } - 6$

Question 32

Find functions f and g so that f $f \circ g = H$

- $$H ( x ) = \left( 5 - 2 x ^ { 3 } \right) ^ { 2 }$$

A) $f ( x ) = 5 - 2 x ^ { 3 } ; g ( x ) = x ^ { 2 }$
B) $f ( x ) = x ^ { 2 } ; g ( x ) = 5 - 2 x ^ { 3 }$
C) $f ( x ) = ( 5 - 2 x ) ^ { 3 } ; g ( x ) = x ^ { 2 }$
D) $f ( x ) = x ^ { 3 } ; g ( x ) = ( 5 - 2 x ) ^ { 2 }$

Question 33

Solve the problem.

-The population P of a predator mammal depends upon the number x of a smaller animal that is its primary food source. The population s of the smaller animal depends upon the amount a of a certain plant that is its
Primary food source. If $$P ( x ) = 3 x ^ { 2 } + 2$$ and s(a) = 2a + 5, what is the relationship between the predator mammal
And the plant food source?

A) $\mathrm { P } ( \mathrm { s } ( \mathrm { a } ) ) = 4 \mathrm { a } ^ { 2 } + 20 \mathrm { a } + 27$
B) $\mathrm { P } ( \mathrm { s } ( \mathrm { a } ) ) = 6 \mathrm { a } + 7$
C) $P ( s ( a ) ) = 12 a ^ { 2 } + 30 a + 77$
D) $\mathrm { P } ( \mathrm { s } ( \mathrm { a } ) ) = 12 \mathrm { a } ^ { 2 } + 60 \mathrm { a } + 77$

Question 34

Decide whether the composite functions, f $$f \circ g$$ nd $\mathbf { g } \circ \mathrm { f }$ f, are equal to x.

- $f ( x ) = \sqrt [ 5 ] { x - 8 } , g ( x ) = x ^ { 5 } + 8$

A) Yes, yes
B) Yes, no
C) No, no
D) No, yes

Question 35

Decide whether the composite functions, f $$f \circ g$$ nd $\mathbf { g } \circ \mathrm { f }$ f, are equal to x.

- $f ( x ) = \sqrt { x } , g ( x ) = x ^ { 2 }$

A) No, no
B) Yes, yes
C) Yes, no
D) No, yes

Question 36

Find functions f and g so that f $f \circ g = H$

- $$\mathrm { H } ( \mathrm { x } ) = \sqrt [ 3 ] { \mathrm { x } + 1 }$$

A) $f ( x ) = \sqrt { x } ; g ( x ) = x + 1$
B) $f ( x ) = \sqrt [ 3 ] { x } ; g ( x ) = x + 1$
C) $f ( x ) = x + 1 ; g ( x ) = \sqrt [ 3 ] { x }$
D) $f ( x ) = \sqrt [ 3 ] { x } ; g ( x ) = 1$

Question 37

Decide whether the composite functions, f $$f \circ g$$ nd $\mathbf { g } \circ \mathrm { f }$ f, are equal to x.

- $f ( x ) = 2 x , \quad g ( x ) = \frac { x } { 2 }$

A) No, no
B) No, yes
C) Yes, no
D) Yes, yes

Question 38

Find functions f and g so that f $f \circ g = H$

- $$H ( x ) = | 9 x + 3 |$$

A) $f ( x ) = | - x | ; \quad g ( x ) = 9 x - 3$
B) $f ( x ) = - | x |$ ; $g ( x ) = 9 x + 3$
C) $f ( x ) = x ; g ( x ) = 9 x + 3$
D) $f ( x ) = | x | ; \quad g ( x ) = 9 x + 3$

Question 39

Decide whether the composite functions, f $$f \circ g$$ nd $\mathbf { g } \circ \mathrm { f }$ f, are equal to x.

- $f ( x ) = x ^ { 3 } + 1 , g ( x ) = \sqrt [ 3 ] { x - 1 }$

A) No, yes
B) No, no
C) Yes, yes
D) Yes, no

Question 40

Find functions f and g so that f $f \circ g = H$

- $$\mathrm { H } ( \mathrm { x } ) = | 3 \mathrm { x } + 7 |$$

A) $f ( x ) = x ; g ( x ) = 3 x + 7$
B) $f ( x ) = | x |$ ;
$g ( x ) = 3 x + 7$
C) $f ( x ) = | - x | ; \quad g ( x ) = 3 x - 7$
D) $f ( x ) = - | x | ; \quad g ( x ) = 3 x + 7$

Question 41

Solve the problem.

Question 42

Find the domain of the composite function f $f ^ { \circ } g$

- $$f ( x ) = \frac { 1 } { x - 7 } ; \quad g ( x ) = \sqrt { x - 1 }$$

A) $\{ x \mid x \geq 1 , x \neq 7 \}$
B) $\{ x \mid x \geq 1 , x \neq 7 , x \neq 50 \}$
C) $\{ x \mid x$ is any real number $\}$
D) $\{ x \mid x \geq 1 , x \neq 50 \}$

Question 43

Find the domain of the composite function f $f ^ { \circ } g$

- $$f ( x ) = \sqrt { x } ; \quad g ( x ) = 5 x + 10$$

A) $\{ x \mid x \geq 0 \}$
B) $\{ x \mid x \leq - 2$ or $x \geq 0 \}$
C) $\{ x \mid x \geq - 2 \}$
D) $\{ x \mid x$ is any real number $\}$

Question 44

Find the domain of the composite function f $f ^ { \circ } g$

- $$f ( x ) = \frac { x } { x + 7 } ; \quad g ( x ) = \frac { 7 } { x + 5 }$$

A) $\{ x \mid x \neq - 5 , x \neq - 6 \}$
B) $\{ x \mid x \neq 0 , x \neq - 5 , x \neq - 6 \}$
C) $\{ x \mid x$ is any real number $\}$
D) $\{ x \mid x \neq - 5 , x \neq - 7 \}$

Question 45

Find the domain of the composite function f $f ^ { \circ } g$

- $$f ( x ) = \frac { - 7 } { x } ; \quad g ( x ) = \frac { - 2 } { x + 1 }$$

A) $\{ x \mid x \neq - 1 \}$
B) $\{ x \mid x \neq - 1 , x \neq 0 \}$
C) $\{ x \mid x$ is any real number $\}$
D) $\{ x \mid x \neq 0 , x \neq - 1 , x \neq 7 \}$

Question 46

Find the domain of the composite function f $f ^ { \circ } g$

- $$f ( x ) = \frac { 6 } { x + 1 } ; \quad g ( x ) = x + 2$$

A) $\{ x \mid x \neq - 3 \}$
B) $\{ x \mid x$ is any real number $\}$
C) $\{ x \mid x \neq - 1 \}$
D) $\{ x \mid x \neq - 1 , x \neq - 2 \}$

Question 47

Solve the problem.

Question 48

Find the domain of the composite function f $f ^ { \circ } g$

- $$f ( x ) = \sqrt { x - 1 } ; \quad g ( x ) = \frac { 1 } { x - 8 }$$

A) $\{ x \mid x \neq 8 , x \neq 1 \}$
B) $\{ x \mid x \geq 1 , x \neq 8 \}$
C) $\{ x \mid x$ is any real number $\}$
D) $\{ x \mid 8 < x \leq 9 \}$

Question 49

Solve the problem.

-The surface area of a balloon is given by $\mathrm { S } ( \mathrm { r } ) = 4 \pi \mathrm { r } ^ { 2 }$ , where $\mathrm { r }$ is the radius of the balloon. If the radius is increasing with time $t$ , as the balloon is being blown up, according to the formula $r ( t ) = \frac { 2 } { 3 } t { } ^ { 3 } , t \geq 0$ , find the surface area $S$ as a function of the time $t .$

A) $S ( r ( t ) ) = \frac { 16 } { 9 } \pi t ^ { 6 }$
B) $S ( r ( t ) ) = \frac { 16 } { 9 } \pi t ^ { 9 }$
C) $S ( r ( t ) ) = \frac { 4 } { 9 } \pi t ^ { 6 }$
D) $S ( r ( t ) ) = \frac { 16 } { 9 } \pi t ^ { 3 }$

Question 50

Find the domain of the composite function f $f ^ { \circ } g$

- $$f ( x ) = x + 8 ; \quad g ( x ) = \frac { 4 } { x + 6 }$$

A) $\{ x \mid x \neq - 14 \}$
B) $\{ x \mid x \neq - 6 \}$
C) $\{ x \mid x \neq - 6 , x \neq - 8 \}$
D) $\{ x \mid x$ is any real number $\}$

Question 51

Find the domain of the composite function f $f ^ { \circ } g$

- $$f ( x ) = 2 x + 2 ; \quad g ( x ) = \sqrt { x }$$

A) $\{ x \mid x$ is any real number $\}$
B) $\{ x \mid x \geq - 1 \}$
C) $\{ x \mid x \geq 0 \}$
D) $\{ x \mid x \leq - 1$ or $x \geq 0 \}$

Question 52

Find the domain of the composite function f $f ^ { \circ } g$

- $$\mathrm { f } ( \mathrm { x } ) = 7 \mathrm { x } + 14 ; \quad \mathrm { g } ( \mathrm { x } ) = \mathrm { x } + 7$$

A) $\{ x \mid x$ is any real number $\}$
B) $\{ x \mid x \neq 9 \}$
C) $\{ x \mid x \neq - 7 , x \neq - 2 \}$
D) $\{ x \mid x \neq - 9 \}$

Question 53

Find the domain of the composite function f $f ^ { \circ } g$

- $$f ( x ) = \sqrt { 2 - x } ; \quad g ( x ) = | 2 x - 1 |$$

A) $\{ x \mid x \leq 2 \}$
B) $\{ x \mid x \geq 2 \}$
C) $\left\{ x \mid - \frac { 1 } { 2 } \leq x \leq \frac { 3 } { 2 } \right\}$
D) all real numbers

Question 54

Solve the problem.

Question 55

Find the domain of the composite function f $f ^ { \circ } g$

- $$f ( x ) = \frac { - 2 } { x + 7 } ; \quad g ( x ) = \frac { - 14 } { x }$$

A) $\{ x \mid x \neq 0 , x \neq - 7 , x \neq 2 \}$
B) $\{ x \mid x$ is any real number $\}$
C) $\{ x \mid x \neq 0 , x \neq - 7 \}$
D) $\{ x \mid x \neq 0 , x \neq 2 \}$

Question 56

Solve the problem.

Question 57

Indicate whether the function is one-to-one.
{(12, -18), (-12, -18), (20, -8)}

A) Yes
B) No

Question 58

Solve the problem.

Question 59

Solve the problem.

-An airline charter service charges a fare per person of $350 plus $20 for each unsold seat. The airplane holds 125 passengers. Let x represent the number of unsold seats and write an expression for the total revenue R for a
Charter flight.

A) $R ( x ) = ( 125 - x ) ( 350 + 20 x )$ or $43,750 + 2,150 x - 20 x ^ { 2 }$
B) $R ( x ) = 125 ( 350 + 20 x )$ or $43,750 + 2,500 x$
C) $R ( x ) = x ( 350 + 20 x )$ or $350 x + 20 x ^ { 2 }$
D) $R ( x ) = ( 125 - x ) ( 350 + 20 x )$ or $43,750 + 2,500 x - 20 x ^ { 2 }$

Question 60

Indicate whether the function is one-to-one.
{(3, -12), (7, 4), (12, -8)}

A) Yes
B) No

Question 61

The graph of a one-to-one function f is given. Draw the graph of the inverse function f-1 as a dashed line or curve.

- $$f ( x ) = \frac { 4 } { x }$$

A) Function is its own inverse


B)

Question 62

Use the horizontal line test to determine whether the function is one-to-one.

A) No
B) Yes

Question 63

Use the horizontal line test to determine whether the function is one-to-one.

A) No
B) Yes

Question 64

Find the inverse of the function and state its domain and range .

- $$\{ ( - 3,4 ) , ( - 1,5 ) , ( 0,2 ) , ( 2,6 ) , ( 5,7 ) \}$$

A) $\{ ( 3,4 ) , ( 1,5 ) , ( 0,2 ) , ( - 2,6 ) , ( - 5,7 ) \} ; \mathrm { D } = \{ 3,1,0 , - 2 , - 5 \} ; \mathrm { R } = \{ 2,4,5,6,7 \}$

B) $\{ ( 3 , - 4 ) , ( 1 , - 5 ) , ( 0 , - 2 ) , ( - 2 , - 6 ) , ( - 5 , - 7 ) \} ; \mathrm { D } = \{ 3,1,0 , - 2 , - 5 \} ; \mathrm { R } = \{ - 7 , - 6 , - 5 , - 4 , - 2 \}$

C) $\{ ( 4 , - 3 ) , ( 5 , - 1 ) , ( 2,0 ) , ( 6,2 ) , ( 7,5 ) \} \mathrm { D } = \{ 2,4,5,6,7 \} ; \mathrm { R } = \{ - 3 , - 1,0,2,5 \}$

D) $\{ ( - 3 , - 4 ) , ( - 1 , - 5 ) , ( 0 , - 2 ) , ( 2 , - 6 ) , ( 5 , - 7 ) \} ; \mathrm { D } = \{ - 3 , - 1,0,2,5 \} ; \mathrm { R } = \{ - 7 , - 6 , - 5 , - 4 , - 2 \}$

Question 65

Use the horizontal line test to determine whether the function is one-to-one.

A) No
B) Yes

Question 66

Use the horizontal line test to determine whether the function is one-to-one.

A) Yes
B) No

Question 67

The graph of a one-to-one function f is given. Draw the graph of the inverse function f-1 as a dashed line or curve.

- $f(x)=2 x$

A)


B)

Question 68

Find the inverse. Determine whether the inverse represents a function.

- $\{ ( 6,5 ) , ( - 1,6 ) , ( - 3,7 ) , ( - 5,8 ) \}$

A) $\{ ( 3,6 ) , ( 4,10 ) , ( 5,8 ) , ( 6,6 ) \} ;$ not a function
B) $\{ ( 4,3 ) , ( 3,8 ) , ( 6,10 ) , ( 4,5 ) \}$ ; not a function
C) $\{ ( 4,3 ) , ( 6,8 ) , ( 6,8 ) , ( 4,5 ) \} ;$ a function
D) $\{ ( 3,6 ) , ( 4,10 ) , ( 5,8 ) , ( 6,6 ) \}$ ; a function

Question 69

The graph of a one-to-one function f is given. Draw the graph of the inverse function f-1 as a dashed line or curve.

- $$f ( x ) = x ^ { 3 } + 4$$

A)


B)

Question 70

Find the inverse of the function and state its domain and range .

- $$\{ ( 9 , - 8 ) , ( 7 , - 7 ) , ( 5 , - 6 ) , ( 3 , - 5 ) \}$$

A) $\{ ( - 7 , - 8 ) , ( - 8,5 ) , ( 9,7 ) , ( - 7 , - 6 ) \} ; \mathrm { D } = \{ ( - 7 , - 8,9 \} ; \mathrm { R } = \{ ( - 8,57 , - 6 \}$

B) $\{ ( - 8,9 ) , ( - 7,7 ) , ( - 6,5 ) , ( - 5,3 ) \} ; \mathrm { D } = \{ - 8 , - 7 , - 6 , - 5 \} ; \mathrm { R } = \{ 9,7,5,3 \}$

C) $\{ ( - 7 , - 8 ) , ( - 5,5 ) , ( 9,5 ) , ( - 7 , - 6 ) \} ; \mathrm { D } = \{ - 7 , - 5,9 \} ; \mathrm { R } = \{ - 8,5 , - 6 \}$

D) $\left\{ \left( 9 , - \frac { 1 } { 8 } \right) , \left( 7 , - \frac { 1 } { 7 } \right) , \left( 5 , - \frac { 1 } { 6 } \right) , \left( 3 , - \frac { 1 } { 5 } \right) \right\} ; \mathrm { D } = \{ 9,7,5,3 \} , \mathrm { R } = \left\{ - \frac { 1 } { 8 } , - \frac { 1 } { 7 } , - \frac { 1 } { 6 } , - \frac { 1 } { 5 } \right\}$

Question 71

Decide whether or not the functions are inverses of each other.

- $$f ( x ) = 4 x + 16 , g ( x ) = \frac { 1 } { 4 } x - 4$$

A) Yes
B) No

Question 72

Use the graph of the given one-to-one function to sketch the graph of the inverse function. For convenience, the graph of
y = x is also given.

-

A)


B)


C)


D)

Question 73

The graph of a one-to-one function f is given. Draw the graph of the inverse function f-1 as a dashed line or curve.

- $$f ( x ) = \sqrt { x + 2 }$$

A)


B)

Question 74

Indicate whether the function is one-to-one.
{(6, -6), (12, -5), (10, -4), (8, -3)}

A) No
B) Yes

Question 75

Indicate whether the function is one-to-one.
{(5, 4), (6, 4), (7, 3), (8, -9)}

A) Yes
B) No

Question 76

Use the horizontal line test to determine whether the function is one-to-one.

A) No
B) Yes

Question 77

Use the horizontal line test to determine whether the function is one-to-one.

A) No
B) Yes

Question 78

Decide whether or not the functions are inverses of each other.

- $$f ( x ) = 8 x - 9 , g ( x ) = \frac { x + 8 } { 9 }$$

A) No
B) Yes

Question 79

Indicate whether the function is one-to-one.
{(7, -3), (3, -7), (-2, 9), (2, -9)}

A) No
B) Yes

Question 80

Find the inverse of the function and state its domain and range .

- $\{ ( - 5 , - 3 ) , ( 3,5 ) , ( 1,1 ) , ( - 1 , - 1 ) \}$

A) $\{ ( - 3 , - 5 ) , ( 5,3 ) , ( 1,1 ) , ( - 1 , - 1 ) \} \mathrm { D } = \{ - 3,5,1 , - 1 \} ; \mathrm { R } = \{ - 5,3,1 , - 1 \}$

B) $\left\{ \left( - 5 , - \frac { 1 } { 3 } \right) , \left( 3 , \frac { 1 } { 5 } \right) , ( 1,1 ) , ( - 1 , - 1 ) \right\} \mathrm { D } = \{ - 5,3,1 , - 1 \} , \mathrm { R } = \left\{ - \frac { 1 } { 3 } , \frac { 1 } { 5 } , 1 , - 1 \right\}$

C) $\{ ( - 1,1 ) , ( 5,3 ) , ( - 3,3 ) , ( 1 , - 1 ) \} ; \mathrm { D } = \{ ( - 1,5 , - 3,1 \} ; \mathrm { R } = \{ 1,3 , - 1 \}$

D) $\{ ( - 1,1 ) , ( 1,3 ) , ( - 3 , - 5 ) , ( 1 , - 1 ) \} ; \mathrm { D } = \{ - 1,1 , - 3,1 \} ; \mathrm { R } = \{ 1,3 , - 5 , - 1 \}$