Deck 9: Logarithmic and Exponential Functions

Question 1

For the given functions f(x) and g(x), find (f + g)(x) or (f - g)(x) as indicated

- $f(x)=7 x-3, g(x)=4 x-7$
Find $(f+g)(x)$ .

A) $-3 \mathrm{x}-4$
B) $11 x+4$
C) $11 \mathrm{x}-10$
D) $3 \mathrm{x}-10$

Answer 1

$11 \mathrm{x}-10$

Question 2

For the given functions f(x) and g(x), find (f + g)(x) or (f - g)(x) as indicated

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

A) $-9 x+12$
B) $-5 \mathrm{x}+12$
C) $-2 \mathrm{x}+5$
D) $3 \mathrm{x}$

Answer 2

$-9 x+12$

Question 3

For the given functions f(x) and g(x), find (f + g)(x) or (f - g)(x) as indicated

- $f(x)=-5 x+8, g(x)=x^{2}-3 x-9$
Find $(f+g)(x)$ .

A) $x^{2}+3 x-1$
B) $x^{2}-8 x-1$
C) $x^{2}-8 x+12$
D) $x^{2}+3 x+5$

Answer 3

$x^{2}-8 x-1$

Question 4

For the given functions f(x) and g(x), find (f + g)(x) or (f - g)(x) as indicated

- $f(x)=2 x^{2}+7 x-5, g(x)=7 x^{2}+3 x+9$
Find $(f+g)(x)$ .

A) $-9 x^{2}+10 x+4$
B) $2 x^{2}+5 x+4$
C) $23 x^{2}$
D) $9 x^{2}+10 x+4$

Question 5

For the given functions f(x) and g(x), find (f + g)(x) or (f - g)(x) as indicated

- $f(x)=5 x-6, g(x)=2 x-4$
Find $(f-g)(x)$ .

A) $7 \mathrm{x}-10$
B) $-3 x+2$
C) $3 x-2$
D) $3 x-10$

Question 6

For the given functions f(x) and g(x), find (f + g)(x) or (f - g)(x) as indicated

- $f(x)=-8 x+8, g(x)=-5 x+9$
Find $(\mathrm{f}-\mathrm{g})(\mathrm{x})$ .

A) $3 \mathrm{x}$
B) $-13 x-1$
C) $-3 x-1$
D) $-3 x+16$

Question 7

For the given functions f(x) and g(x), find (f + g)(x) or (f - g)(x) as indicated

- $f(x)=-5 x^{2}-18 x, g(x)=-11 x^{2}-20 x+3$
Find $(f-g)(x)$ .

A) $6 x^{2}-38 x-3$
B) $-16 x^{2}-38 x+3$
C) $8 x^{2}-3$
D) $6 x^{2}+2 x-3$

Question 8

For the given functions $f(x)$ and $g(x)$ , find $(f \cdot g)(x)$ or $\left(\frac{f}{g}\right)(x)$ as indicated.

- $f(x)=x+4, g(x)=x+7$
Find $(f \cdot g)(x)$ .

A) $x^{2}+11 x+11$
B) $x^{2}+8 x+28$
C) $x^{2}+11 x+28$
D) $x^{2}+28$

Question 9

For the given functions $f(x)$ and $g(x)$ , find $(f \cdot g)(x)$ or $\left(\frac{f}{g}\right)(x)$ as indicated.

- $f(x)=2 x-8, g(x)=7 x-3$
Find $(f \cdot g)(x)$ .

A) $14 x^{2}-59 x+24$
B) $14 x^{2}+24$
C) $14 x^{2}-62 x+24$
D) $9 x^{2}-62 x-11$

Question 10

For the given functions $f(x)$ and $g(x)$ , find $(f \cdot g)(x)$ or $\left(\frac{f}{g}\right)(x)$ as indicated.

- $f(x)=-2 x, g(x)=10 x-5$
Find $(f \cdot g)(x)$ .

A) $10 x^{2}+10 x$
B) $-10 x^{2}$
C) $-20 x^{2}+10 x$
D) $-20 x^{2}-5$

Question 11

For the given functions $f(x)$ and $g(x)$ , find $(f \cdot g)(x)$ or $\left(\frac{f}{g}\right)(x)$ as indicated.

- $f(x)=-9 x+4, g(x)=5 x^{2}-x+4$
Find $(\mathrm{f} \cdot \mathrm{g})(\mathrm{x})$ .

A) $-45 x^{3}-40 x+16$
B) $-45 x^{3}+11 x^{2}-40 x+16$
C) $14 x^{2}-40 x+16$
D) $-45 x^{3}+29 x^{2}-40 x+16$

Question 12

For the given functions $f(x)$ and $g(x)$ , find $(f \cdot g)(x)$ or $\left(\frac{f}{g}\right)(x)$ as indicated.

- $f(x)=4 x^{2}+2 x+4, g(x)=x^{2}-4 x+5$
Find $(f \cdot g)(x)$ .

A) $4 x^{4}-16 x^{3}+12 x^{2}-6 x+20$
B) $4 x^{4}-16 x^{3}+16 x^{2}-6 x+20$
C) $4 x^{4}-14 x^{3}+16 x^{2}-6 x+20$
D) $4 x^{4}-14 x^{3}+12 x^{2}-6 x+20$

Question 13

For the given functions $f(x)$ and $g(x)$ , find $(f \cdot g)(x)$ or $\left(\frac{f}{g}\right)(x)$ as indicated.

- $f(x)=2 x+1, g(x)=x-7$
Find $\left(\frac{f}{g}\right)(x)$ .

A) $\frac{2 x+1}{x-7}$

B) $\frac{x-7}{2 x+1}$

C) $2-\frac{x}{7}$

D) $2 x-\frac{1}{7}$

Question 14

For the given functions $f(x)$ and $g(x)$ , find $(f \cdot g)(x)$ or $\left(\frac{f}{g}\right)(x)$ as indicated.

- $f(x)=x+4, g(x)=2 x-7$
Find $\left(\frac{f}{g}\right)(x)$ .

A) $\frac{2 x-7}{x+4}$

B) $\frac{x}{2}-\frac{4}{7}$

C) $\frac{x+4}{2 x-7}$

D) $\frac{x}{2 x-7}+4$

Question 15

For the given functions $f(x)$ and $g(x)$ , find $(f \cdot g)(x)$ or $\left(\frac{f}{g}\right)(x)$ as indicated.

- $f(x)=x^{2}+8 x+12, g(x)=x+6$
Find $\left(\frac{f}{g}\right)(x)$ .

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

Question 16

For the given functions $f(x)$ and $g(x)$ , find $(f \cdot g)(x)$ or $\left(\frac{f}{g}\right)(x)$ as indicated.

- $f(x)=x^{2}+2 x-15, g(x)=x+5$
Find $\left(\frac{f}{g}\right)(x)$ .

A) $\mathrm{x}-3$
B) $x^{2}+3 x-10$
C) $x+3$
D) $x^{2}-3$

Question 17

Solve the problem.

-Find $(f+g)(4)$ when $f(x)=x+7$ and $g(x)=x+1$ .

A) 0
B) 14
C) 16
D) 2

Question 18

Solve the problem.

-Find $(f+g)(-2)$ when $f(x)=-2 x^{3}-3 x-35$ and $g(x)=5 x^{2}+2 x$

A) 3
B) -7
C) -27
D) -9

Question 19

Solve the problem.

-Find (f - g)(4) when $f(x)=3 x^{2}+5$ and $g(x)=x+1$ .

A) 56
B) 50
C) -57
D) 48

Question 20

Solve the problem.

-Find $(f \cdot g)(2)$ when $f(x)=x-6$ and $g(x)=-3 x^{2}+12 x-4$ .

A) -96
B) -32
C) 64
D) -128

Question 21

Solve the problem.

-Find $\left(\frac{f}{g}\right)(4)$ when $f(x)=x-5$ and $g(x)=7 x+1$ .

A) $-\frac{1}{28}$

B) $-\frac{3}{8}$

C) $-\frac{1}{32}$

D) $-\frac{1}{29}$

Question 22

Solve the problem.

-Find $\left(\frac{f}{g}\right)(-2)$ when $f(x)=2 x-7$ and $g(x)=4 x^{2}+14 x+3$ .

A) $-\frac{4}{3}$

B) $-\frac{4}{9}$

C) $-\frac{2}{9}$

D) $\frac{11}{9}$

Question 23

Solve the problem.

-The function $\mathrm{w}(\mathrm{x})=5 \mathrm{x}-3$ describes a company's monthly costs in wages and $\mathrm{p}(\mathrm{x})=2 \mathrm{x}-9$ describes the cost of production, where $x$ represents the number of units produced. Find the function $\mathrm{c}(\mathrm{x})$ that describes the total cost of producing $\mathrm{x}$ units.

A) $c(x)=3 x-12$
B) $c(x)=7 x+6$
C) $\mathrm{c}(\mathrm{x})=7 \mathrm{x}-12$
D) $c(x)=3 x+6$

Question 24

Solve the problem.

-The function $P(x)=-0.3 x^{2}+50 x-14$ describes a company's net monthly profit or loss and the function $\mathrm{C}(\mathrm{x})=9 \mathrm{x}+14$ describes its monthly costs, where $\mathrm{x}$ represents the number of units produced. The total revenue function, $\mathrm{R}(\mathrm{x})$ , is such that $\mathrm{R}(\mathrm{x})=\mathrm{C}(\mathrm{x})+\mathrm{P}(\mathrm{x})$ . Find $\mathrm{R}(\mathrm{x})$ .

A) $\mathrm{R}(\mathrm{x})=61 \mathrm{x}-0.3 \mathrm{x}^{2}$
B) $R(x)=59 x+0.3 x^{2}$
C) $R(x)=58 x-0.6 x^{2}$
D) $R(x)=59 x-0.3 x^{2}$

Question 25

Solve the problem.

-The number of male lawyers, in thousands, in a certain country in a particular year can be approximated by the function $\mathrm{f}(\mathrm{x})=11.1 \mathrm{x}+215$ , where $\mathrm{x}$ represents the number of years after 1995. The number of female lawyers, in thousands, in a certain country in a particular year can be approximated by the function $\mathrm{g}(\mathrm{x})=10.1 \mathrm{x}+143$ , where again $\mathrm{x}$ represents the number of years after 1995.
(i) Find $(f+g)(x)$ . Explain, in your own words, what this function represents.
(ii) Find $(f+g)(45)$ . Explain, in your own words, what this number represents.

A) (i) $(\mathrm{f}+\mathrm{g})(\mathrm{x})=154.1 \mathrm{x}+225.1$ ; this is the total number of lawyers, in thousands, in a certain country x years after 1995 .
(ii) 7159.6; there will be 7,159,600 lawyers in a certain country in the year 2040.
B) (i) $(\mathrm{f}+\mathrm{g})(\mathrm{x})=379.2 \mathrm{x}$ ; this is the total number of lawyers, in thousands, in a certain country $\mathrm{x}$ years after 1995.
(ii) 17,064; there will be 17,064,000 lawyers in a certain country in the year 2040.
C) (i) $(\mathrm{f}+\mathrm{g})(\mathrm{x})=21.2 \mathrm{x}+358$ ; this is the total number of lawyers, in thousands, in a œrtain country x years after 1995.
(ii) 1312; there will be 1,312,000 lawyers in a certain country in theyear 2040.
D) (i) $(\mathrm{f}+\mathrm{g})(\mathrm{x})=226.1 \mathrm{x}+153.1$ ; this is the total number of lawyers, in thousands, in a certain country x years after 1995 .
(ii) 10,327.6; there will be 10,327,600 lawyers in a certain country in the year 2040.

Question 26

Solve the problem.

-The amount of money, in billions of dollars, spent on health care that was covered by insurance in a certain country in a particular year can be approximated by the function $\mathrm{f}(\mathrm{x})=\mathrm{x}^{2}+19 \mathrm{x}+293$ , where $x$ represents the number of years after 1995. The amount of money, in billions of dollars, spent on health care that was paid out of pocket in a certain country in a particular year can be approximated by the function $\mathrm{g}(\mathrm{x})=5 \mathrm{x}+142$ , where again $\mathrm{x}$ represents the number of years after 1995.
(i) Find ( $\mathrm{f}-\mathrm{g})(\mathrm{x})$ . Explain, in your own words, what this function represents.
(ii) Find ( $\mathrm{f}-\mathrm{g})(55)$ . Explain, in your own words, what this number represents.

A) (i) ( $\mathrm{f}-\mathrm{g})(\mathrm{x})=\mathrm{x}^{2}+14 \mathrm{x}+151$ ; this is the difference between health- care costs covered by insurance and health- care costs that are paid out of pocket, in billions of dollars, $x$ years after 1995.
(ii) 3946; health- care costs covered by insurance will be $\$ 3,946,000,000,000$ higher than health- care costs that are paid out of pocket in 2050.
B) (i) (f - g) $(x)=x^{2}-24 x-435$ ; this is the difference between health- care costs covered by insurance and health- care costs that are paid out of pocket, in billions of dollars, $\mathrm{x}$ years after 1995.
(ii) 1270; health- care costs covered by insurance will be $\$ 1,270,000,000,000$ higher than health- care costs that are paid out of pocket in 2050.
C) (i) (f - g)(x) $=x^{2}-24 x-435$ ; this is the difference between health- care costs that are paid out of pocket and those that are covered by insurance, in billions of dollars, $\mathrm{x}$ years after 1995.
(ii) 1270; health- care costs covered by insurance will be $\$ 1,270,000,000,000$ less than heal th- care costs that are paid out of pocket in 2050.
D) (i) (f - g) $(x)=x^{2}+14 x+151$ ; this is the difference between health- care costs that are paid out of pocket and those that are covered by insurance, in billions of dollars, $\mathrm{x}$ years after 1995.
(ii) 3946; health- care costs covered by insurance will be $\$ 3,946,000,000,000$ less than heal th- care costs that are paid out of pocket in 2050.

Question 27

Given $f(x)$ and $g(x)$ , find the indicated composition and evaluate.

- $f(x)=6 x+2 ; g(x)=x+7$
Find $(f \circ g)(4)$ .

A) 68
B) 37
C) 33
D) 286

Question 28

Given $f(x)$ and $g(x)$ , find the indicated composition and evaluate.

- $f(x)=7 x+9 ; g(x)=5 x+5$
Find $(\mathrm{f} \circ \mathrm{g})(4)$ .

A) 190
B) 62
C) 184
D) 925

Question 29

Given $f(x)$ and $g(x)$ , find the indicated composition and evaluate.

- $f(x)=x^{2}+2 ; g(x)=4 x+5$
Find $(\mathrm{g} \circ \mathrm{f})(7)$ .

A) 199
B) 56
C) 209
D) 1091

Question 30

Given $f(x)$ and $g(x)$ , find the indicated composition and evaluate.

- $f(x)=x-6 ; g(x)=-7 x^{2}-8 x-7$
Find (f $\circ \mathrm{g})(4)$ .

A) -2419
B) -408
C) -277
D) -912

Question 31

Given $f(x)$ and $g(x)$ , find the indicated composition and evaluate.

- $f(x)=-8 x+7 ; g(x)=-9 x^{2}+7 x-2$
Find $(\mathrm{g} \circ \mathrm{of})(6)$ .

A) 2279
B) 119
C) $-15,418$
D) 80

Question 32

Given $f(x)$ and $g(x)$ , find the indicated composition and state its domain.

- $f(x)=6 x+5, g(x)=4 x-1$
Find $(\mathrm{f} \circ \mathrm{g})(\mathrm{x})$ .

A) $24 x+4$ , all real numbers
B) $24 x+19$ , all real numbers
C) $24 x+11$ , all real numbers
D) $24 \mathrm{x}-1$ , all real numbers

Question 33

Given $f(x)$ and $g(x)$ , find the indicated composition and state its domain.

- $f(x)=8 x+7, g(x)=4 x-1$
Find $(\mathrm{g} \circ \mathrm{f})(\mathrm{x})$ .

A) $32 x+15$ , all real numbers
B) $32 x+6$ , all real numbers
C) $32 x+27$ , all real numbers
D) $32 x$ - 1, all real numbers

Question 34

Given $f(x)$ and $g(x)$ , find the indicated composition and state its domain.

- $f(x)=-4 x+4, g(x)=2 x+8$
Find $(\mathrm{g} \circ \mathrm{f})(\mathrm{x})$ .

A) $-8 x+36$ , all real numbers
B) $-8 x+16$ , all real numbers
C) $x+16$ , all real numbers
D) - $8 x-0$ , all real numbers

Question 35

Given $f(x)$ and $g(x)$ , find the indicated composition and state its domain.

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

A) $4 x^{2}+16 x+16$ , all real numbers
B) $4 x^{2}+8 x+10$ , all real numbers
C) $2 x^{2}-8$ , all real numbers
D) $4 x^{2}+16 x+10$ , all real numbers

Question 36

Given $f(x)$ and $g(x)$ , find the indicated composition and state its domain.

- $f(x)=4 x^{2}+2 x+3, g(x)=2 x-8$
Find $(\mathrm{g} \circ \mathrm{f})(\mathrm{x})$ .

A) $4 x^{2}+4 x-2$ , all real numbers
B) $4 x^{2}+2 x-5$ , all real numbers
C) $8 x^{2}+4 x+14$ , all real numbers
D) $8 x^{2}+4 x-2$ , all real numbers

Question 37

Given $f(x)$ and $g(x)$ , find the indicated composition and state its domain.

- $f(x)=\frac{x-5}{3} ; g(x)=3 x+5$
Find $(\mathrm{g} \circ \mathrm{f})(\mathrm{x})$ .

A) $x$ , all real numbers
B) $x-\frac{5}{3}$ , all real numbers
C) $x+10$ , all real numbers
D) $3 x+10$ , all real numbers

Question 38

Given $f(x)$ and $g(x)$ , find the indicated composition and state its domain.

- $f(x)=\frac{9}{x} ; g(x)=5 x^{2}$
Find $(\mathrm{g} \circ \mathrm{f})(\mathrm{x})$ .

A) $\frac{9}{5 x^{2}}$ , all real numbers except 0

B) $\frac{5 x^{2}}{9}$ , all real numbers

C) $\frac{405}{x^{2}}$ , all real numbers except 0

D) $\frac{5 x^{2}}{81}$ , all real numbers

Question 39

Given $f(x)$ and $g(x)$ , find the indicated composition and state its domain.

- $f(x)=\frac{2}{x^{2}} ; g(x)=x-5$
Find $(\mathrm{g} \circ \mathrm{f})(\mathrm{x})$ .

A) $\frac{2}{(x-5)^{2}}$ , all real numbers exœpt 5

B) $\frac{2}{x^{2}-5}$ , all real numbers except $\sqrt{5}$

C) $\frac{2}{x^{2}}-5$ , all real numbers except 0

D) $\frac{-3}{x^{2}}$ , all real numbers except 0

Question 40

Given $f(x)$ and $g(x)$ , find the indicated composition and state its domain.

- $f(x)=\frac{2 x+3}{5 x-8}, g(x)=x-8$
Find $(\mathrm{f} \circ g)(\mathrm{x})$ and state its domain.

A) $\frac{2 x+13}{5 x+48}$ , all real numbers except $-\frac{48}{5}$ .

B) $\frac{2 x-13}{5 x-48}$ , all real numbers exœpt $\frac{48}{5}$ .

C) $\frac{2 x+5}{5 x+16}$ , all real numbers except $-\frac{16}{5}$ .

D) $\frac{2 x-5}{5 x-16}$ , all real numbers except $\frac{16}{5}$ .

Question 41

Given $f(x)$ and $g(x)$ , find the indicated composition and state its domain.

- $f(x)=\sqrt{2 x+11}, g(x)=x-12$
Find (f $\circ g)(x)$ and state its domain.

A) $\sqrt{2 x-13}$ , all real numbers except $\frac{13}{2}$

B) $\sqrt{2 x+13},\left[-\frac{13}{2}, \infty\right)$

C) $\sqrt{2 x-13},\left[\frac{13}{2}, \infty\right)$

D) $\sqrt{2 x+13}$ , all real numbers exœet $-\frac{13}{2}$

Question 42

Express $h(x)$ as a composition of two functions $f(x)$ and $g(x)$ : (f $\circ g)(x)$ . A nsw ers may vary. Choose the possible answer.

- $h(x)=8(x+2)^{3}$

A) $f(x)=8 x^{2}, g(x)=x^{2}+2 x$
B) $f(x)=x^{3}, g(x)=8 x+16$
C) $f(x)=8 x^{3}+2, g(x)=x$
D) $f(x)=8 x^{3}, g(x)=x+2$

Question 43

Express $h(x)$ as a composition of two functions $f(x)$ and $g(x)$ : (f $\circ g)(x)$ . A nsw ers may vary. Choose the possible answer.

- $h(x)=5 \sqrt{6 x-17}+10$

A) $f(x)=5 \sqrt{x+10}, g(x)=6 x-17$
B) $f(x)=5 \sqrt{x}+10, g(x)=6 x-17$
C) $f(x)=5 \sqrt{x}, g(x)=6 x-7$
D) $f(x)=5 \sqrt{x+10}, g(x)=6 x-7$

Question 44

Given $g(x)$ and $(g \circ f)(x)$ , find $f(x)$ .

- $g(x)=\frac{3}{4} x+2,(g \circ f)(x)=12 x+23$

A) $f(x)=12 x+20$
B) $f(x)=8 x+14$
C) $f(x)=18 x+32$
D) $f(x)=16 x+28$

Question 45

Given $g(x)$ and $(g \circ f)(x)$ , find $f(x)$ .

- $g(x)=2 x^{2}-7,(g \circ f)(x)=2 x^{2}-20 x+43$

A) $f(x)=x-5$
B) $f(x)=x+7$
C) $f(x)=x+3$
D) $f(x)=x-4$

Question 46

For the piecewise function $f(x)=\left\{\begin{array}{ll}x+3 & \text { if } x \leq-4 \\ -2 x+9 & \text { if } x>-4\end{array}\right.$ , find $(f \circ f)(-6)$ .

A) 3
B) 9
C) -3
D) 15

Question 47

For the piecewise function $f(x)=\left\{\begin{array}{l}-|x+3|+14 \text { if } x \leq 7 \\ \sqrt{x-5}-10 \text { if } x>7\end{array}\right.$ , find $(f \circ f \circ f)(2)$ .

A) 12
B) 9
C) 19
D) -8

Question 48

Use the graph of the piecewise function f(x) to find the following

- $(f \circ f)(-3)$

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

Question 49

Use the graph of the piecewise function f(x) to find the following

- $(f \circ f \circ f)(1)$

A) 9
B) -3
C) 3
D) -5

Question 50

Find the specified domain

-For $f(x)=2 x-5$ and $g(x)=\sqrt{x+8}$ , what is the domain of $f \circ g$ ?

A) $(-8,8)$
B) $[-8, \infty)$
C) $[0, \infty)$
D) $[8, \infty)$

Question 51

Find the specified domain

-For $f(x)=2 x-5$ and $g(x)=\sqrt{x+2}$ , what is the domain of $g$ of?

A) $[\infty, 1.5)$
B) $[2, \infty)$
C) $(-2,2)$
D) $[1.5, \infty)$

Question 52

Find the specified domain

-For $f(x)=x^{2}-1$ and $g(x)=2 x+3$ , what is the domain of $f \circ g$ ?

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

Question 53

Find the specified domain

-For $g(x)=\sqrt{x+3}$ and $h(x)=\frac{1}{x-4}$ , what is the domain of $h \circ g$ ?

A) $[-3, \infty)$
B) $[-3,13) \cup(13, \infty)$
C) $[0,13) \cup(13, \infty)$
D) $[-3,4) \cup(4, \infty)$

Question 54

Find the specified domain

-For $f(x)=7 x-7$ and $g(x)=8 x+6$ , what is the domain of $f \circ g$ ?

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

Question 55

Find the specified domain

-For $f(x)=\frac{6}{x^{2}}$ and $g(x)=4-x$ , what is the domain of $f \circ g$ ?

A) $(-\infty, 4) \cup(4, \infty)$
B) $(-\infty, 0) \cup(0, \infty)$
C) $(-\infty, 0) \cup(0,4) \cup(4, \infty)$
D) $(-\infty, \infty)$

Question 56

Find the specified domain

-For $f(x)=5 \sqrt{x+2}$ and $g(x)=4 x+18$ , what is the domain of $f \circ g$ ?

A) $[5, \infty)$
B) $[-2, \infty)$
C) $(-\infty,-5]$
D) $[-5, \infty)$

Question 57

Find the specified domain

-For $f(x)=3 \sqrt{x+5}$ and $g(x)=2 x+15$ , what is the domain of $g$ of?

A) $(-\infty, \infty)$
B) $(-5, \infty)$
C) $[-5, \infty)$
D) $[-20, \infty)$

Question 58

Find the specified domain

-For $f(x)=\frac{1}{x-4}$ and $g(x)=\frac{3}{x}$ , what is the domain of $f \circ g$ ?

A) $\left(0, \frac{3}{4}\right) \cup\left(\frac{3}{4}, \infty\right)$
B) $(-\infty, 0) \cup(0, \infty)$
C) $(-\infty, 0) \cup(0,4) \cup(4, \infty)$
D) $(-\infty, 0) \cup\left(0, \frac{3}{4}\right) \cup\left(\frac{3}{4}, \infty\right)$

Question 59

Find the specified domain

-For $f(x)=\frac{1}{x-2}$ and $g(x)=\frac{7}{x}$ , what is the domain of $g \circ f$ ?

A) $(-\infty, 0) \cup\left(0, \frac{7}{2}\right) \cup\left(\frac{7}{2}, \infty\right)$
B) $(-\infty, 2) \cup(2, \infty)$
C) $(-\infty, 0) \cup(0, \infty)$
D) $(-\infty, 0) \cup(0,2) \cup(2, \infty)$

Question 60

A fixed point of a function $f(x)$ is a value for which $f(x)=x$ . For the given function, find:
a) Fixed point of $f(x)$
b) (f $\circ f)(\mathbf{x})$
c) Fixed point of (f $\circ\mathbf{f})(\mathbf{x})$

- $f(x)=2 x-5$

A) a) 5 b) $4 \mathrm{x}-15$ c) 5
B) a) 1 b) $4 \mathrm{x}-1$ c) 3
C) a) 1 b) $4 \mathrm{x}-3$ c) 1
D) a) -5 b) $4 \mathrm{x}+15$ c) -5

Question 61

A fixed point of a function $f(x)$ is a value for which $f(x)=x$ . For the given function, find:
a) Fixed point of $f(x)$
b) (f $\circ f)(\mathbf{x})$
c) Fixed point of (f $\circ\mathbf{f})(\mathbf{x})$

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

A) a) 2 b) $3 x-1$ c) 5
B) a) 8 b) $\frac{1}{4} x-3$ c) -1
C) a) 11 b) $3 x-1$ c) 11
D) a) 4 b) $\frac{1}{4} \mathrm{x}+3$ c) 4

Question 62

For the given functions $f(x)$ and $g(x)$ , find a value $x$ for which $(f\circ g)(x)=(g\circ f)(x)$ .

- $f(x)=x^{2}+9 x+7, g(x)=x+2$

A) $x=-\frac{5}{2}$
B) $x=5$
C) $x=-5$
D) $\mathrm{x}=2$

Question 63

For the given functions $f(x)$ and $g(x)$ , find a value $x$ for which $(f\circ g)(x)=(g\circ f)(x)$ .

- $f(x)=x^{2}+7 x-4, g(x)=x-6$

A) $x=\frac{3}{2}$
B) $x=0$
C) $x=7$
D) $x=-1$

Question 64

For the given functions $f(x)$ and $g(x)$ , find a value $x$ for which $(f\circ g)(x)=(g\circ f)(x)$ .

- $f(x)=x+6, g(x)=x^{2}-16$

A) $x=-\frac{7}{2}$

B) $x=\frac{13}{2}$

C) $x=\frac{7}{2}$

D) $x=-\frac{5}{2}$

Question 65

For the given functions $f(x)$ and $g(x)$ , find a value $x$ for which $(f\circ g)(x)=(g\circ f)(x)$ .

- $f(x)=x-3, g(x)=5 x^{2}-8 x+5$

A) $x=\frac{11}{5}$

B) $x=\frac{4}{5}$

C) $x=-\frac{12}{5}$

D) $x=\frac{12}{5}$

Question 66

For the given function $g(x)$ , find a function $f(x)$ such that $(f \circ g)(x)=x$ .

- $g(x)=x+5$

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

Question 67

For the given function $g(x)$ , find a function $f(x)$ such that $(f \circ g)(x)=x$ .

- $g(x)=-18 x$

A) $f(x)=18 x$

B) $f(x)=-\frac{x}{18}$

C) $f(x)=-\frac{x}{18}$ .

D) $f(x)=-\frac{18}{x}$

Question 68

For the given function $g(x)$ , find a function $f(x)$ such that $(f \circ g)(x)=x$ .

- $g(x)=4 x+7$

A) $f(x)=\frac{7}{4} x$
B) $f(x)=\frac{x-4}{7}$
C) $f(x)=\frac{x-7}{4}$
D) $f(x)=\frac{x+7}{4}$

Question 69

Determine whether the graph is the graph of a function.

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Question 70

Determine whether the graph is the graph of a function.

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Question 71

Determine whether the graph is the graph of a function.

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Question 72

Determine whether the graph is the graph of a function.

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Question 73

Determine whether the graph is the graph of a function.

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Question 74

Determine whether the graph is the graph of a function.

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Question 75

Determine whether the graph is the graph of a function.

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Question 76

Determine whether the graph is the graph of a function.

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Question 77

Determine whether function is one-to-one.

- $\begin{array}{l|l|l|l}\mathrm{x} & -17 & 17 & 6 \\\hline \mathrm{f}(\mathrm{x}) & 8 & -3 & -14 \\\hline\end{array}$

Question 78

Determine whether function is one-to-one.

- $\begin{array}{c|c|c|c|c}\mathrm{x} & -2 & -1 & 0 & 1 \\\hline \mathrm{f}(\mathrm{x}) & -6 & -6 & 2 & -1 \\\hline\end{array}$

Question 79

Determine whether function is one-to-one.

- $\{(-5,4),(-18,11),(-19,-8)\}$

Question 80

Determine whether function is one-to-one.

- $\{(13,4),(-2,4),(-7,-12)\}$