Question 1

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

Accepted Answer

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

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

Accepted Answer

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 
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 3

Use a calculator to approximate the natural logarithm to four decimal places.
-ln 205

Accepted Answer

A)  $0.1873$ 
B)  $75.6458$ 
C)  $5.3230$ 
D)  $2.3118$ 
A)  $0.1873$ 
B)  $75.6458$ 
C)  $5.3230$ 
D)  $2.3118$

Question 4

Find the exact value.
-$\ln \mathrm { e } ^ { 3 }$

Accepted Answer

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

Question 5

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

Accepted Answer

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)  $\left( \frac { f } { g } \right) ( x ) = \frac { 1 - 4 x } { \sqrt { x } } , \text { where } x \neq 0$ 
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 6

Determine whether the function is one-to-one. If it is one-to-one find an equation or a set of ordered pairs that defines
the inverse function of the given function.
-$$f ( x ) = 5 - 4 x$$

Accepted Answer

A)  one-to-one; $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 1 } { 5 - 4 \mathrm { x } }$ 
B)  one-to-one; $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { - \mathrm { x } + 5 } { 4 }$ 
C)  one-to-one; $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { \mathrm { x } - 5 } { 4 }$ 
D)  not one-to-one 
A)  one-to-one; $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 1 } { 5 - 4 \mathrm { x } }$ 
B)  one-to-one; $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { - \mathrm { x } + 5 } { 4 }$ 
C)  one-to-one; $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { \mathrm { x } - 5 } { 4 }$ 
D)  not one-to-one

Question 7

Solve.
-The population in a particular country is growing at the rate of $1.3 \%$ per year. If $7,638,000$ people lived there in 1999 , how many will there be in the year 2007? Use $\mathrm { y } = \mathrm { y } _ { 0 } \mathrm { e } ^ { 0.013 \mathrm { t } }$ and round to the nearest ten-thousand.

Accepted Answer

A)  $8,310,000$ 
B)  $9,320,000$ 
C)  $8,480,000$ 
D)  $10,170,000$ 
A)  $8,310,000$ 
B)  $9,320,000$ 
C)  $8,480,000$ 
D)  $10,170,000$

Question 8

Find the value of the logarithmic expression.
-$\log _ { 64 } 8$

Accepted Answer

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

Question 9

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

Accepted Answer

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)  $\left( \frac { f } { g } \right) ( x ) = 2 x ^ { 4 } , \text { where } x \neq 0$ 
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 10

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

Accepted Answer

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)  $f ( x ) = | x | ; g ( x ) = 6 - 7 x ^ { 2 }$ 
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 11

Solve for x.
-$\log _ { 10 } x = 1$

Accepted Answer

A)  $\left\{ \frac { 1 } { 10 } \right\}$ 
B)  $\{ 0 \}$ 
C)  $\{ 1 \}$ 
D)  $\{ 10 \}$ 
A)  $\left\{ \frac { 1 } { 10 } \right\}$ 
B)  $\{ 0 \}$ 
C)  $\{ 1 \}$ 
D)  $\{ 10 \}$

Question 12

Solve the equation.
-$\log _ { 5 } x + \log _ { 5 } ( x - 24 ) = 2$

Accepted Answer

A)  $\{ 25 \}$ 
B)  $\{ 1 , - 25 \}$ 
C)  $\{ - 1,25 \}$ 
D)  $\{ 5 \}$ 
A)  $\{ 25 \}$ 
B)  $\{ 1 , - 25 \}$ 
C)  $\{ - 1,25 \}$ 
D)  $\{ 5 \}$

Question 13

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

Accepted Answer

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

Question 14

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

Accepted Answer

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)  $\left( \frac { f } { g } \right) ( x ) = \frac { 3 x + 4 } { 5 x - 1 } , \text { where } x \neq \frac { 1 } { 5 }$ 
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 15

Write as a logarithmic equation.
-$$2 ^ { 3 } = 8$$

Accepted Answer

A)  $\log _ { 2 } 3 = 8$ 
B)  $\log _ { 8 } 2 = 3$ 
C)  $\log _ { 3 } 8 = 2$ 
D)  $\log _ { 2 } 8 = 3$ 
A)  $\log _ { 2 } 3 = 8$ 
B)  $\log _ { 8 } 2 = 3$ 
C)  $\log _ { 3 } 8 = 2$ 
D)  $\log _ { 2 } 8 = 3$

Question 16

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

Accepted Answer

A)  $F ( x ) = ( g \circ h ) ( x )$ 
B)  $F ( x ) = ( g \circ f ) ( x )$ 
C)  $F ( x ) = ( h \circ g ) ( x )$ 
D)  $F ( x ) = ( f \circ g ) ( x )$ 
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 17

Solve the equation. Give an approximate solution to four decimal places.
-$$e ^ { ( x + 2 ) = 5 }$$

Accepted Answer

A)  $\{ - 0.2953 \}$ 
B)  $\{ - 0.0541 \}$ 
C)  $\{ 1.9459 \}$ 
D)  $\{ - 0.3906 \}$ 
A)  $\{ - 0.2953 \}$ 
B)  $\{ - 0.0541 \}$ 
C)  $\{ 1.9459 \}$ 
D)  $\{ - 0.3906 \}$

Question 18

Provide an appropriate response.
-Solve $\ln ( 3 x + 8 ) = 1.37$ accurate to four decimal places.

Accepted Answer

A)  $\{ 3.9785 \}$ 
B)  $\{ - 2.5617 \}$ 
C)  $\{ - 1.3549 \}$ 
D)  $\{ 0.0004 \}$ 
A)  $\{ 3.9785 \}$ 
B)  $\{ - 2.5617 \}$ 
C)  $\{ - 1.3549 \}$ 
D)  $\{ 0.0004 \}$

Question 19

Solve the equation.
-$$\log _ { 9 } 8 + \log _ { 9 } x = 1$$

Accepted Answer

A)  $\left\{ \frac { 8 } { 9 } \right\}$ 
B)  $\left\{ \frac { 9 } { 8 } \right\}$ 
C)  $\{ \sqrt [ 8 ] { 9 } \}$ 
D)  $\left\{ \frac { 1 } { 8 } \right\}$ 
A)  $\left\{ \frac { 8 } { 9 } \right\}$ 
B)  $\left\{ \frac { 9 } { 8 } \right\}$ 
C)  $\{ \sqrt [ 8 ] { 9 } \}$ 
D)  $\left\{ \frac { 1 } { 8 } \right\}$

Question 20

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

Accepted Answer

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

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

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

Use a calculator to approximate the natural logarithm to four decimal places. -ln 205

Find the exact value. - $\ln \mathrm { e } ^ { 3 }$

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

Determine whether the function is one-to-one. If it is one-to-one find an equation or a set of ordered pairs that defines the inverse function of the given function. - $f ( x ) = 5 - 4 x$

Solve. -The population in a particular country is growing at the rate of $1.3 \%$ per year. If $7,638,000$ people lived there in 1999 , how many will there be in the year 2007? Use $\mathrm { y } = \mathrm { y } _ { 0 } \mathrm { e } ^ { 0.013 \mathrm { t } }$ and round to the nearest ten-thousand.

Find the value of the logarithmic expression. - $\log _ { 64 } 8$

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

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

Solve for x. - $\log _ { 10 } x = 1$

Solve the equation. - $\log _ { 5 } x + \log _ { 5 } ( x - 24 ) = 2$

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

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

Write as a logarithmic equation. - $2 ^ { 3 } = 8$

Write the function F(x) as a composition of f, g, or h. - f(x)=-4g(x)=5xh(x)= F(x)=25-4

Solve the equation. Give an approximate solution to four decimal places. - $e ^ { ( x + 2 ) = 5 }$

Provide an appropriate response. -Solve $\ln ( 3 x + 8 ) = 1.37$ accurate to four decimal places.

Solve the equation. - $\log _ { 9 } 8 + \log _ { 9 } x = 1$

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

Real Numbers and Algebraic Expressions

Equations, Inequalities, and Problem Solving

Graphs and Functions

Systems of Equations and Inequalities

Polynomials and Polynomial Functions

Rational Expressions

Rational Exponents, Radicals, and Complex Numbers

Quadratic Equations and Functions

Conic Sections

Fractions

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Exam 9: Exponential and Logarithmic Functions

f(x)=x+2;g(x)=8x2f ( x ) = x + 2 ; g ( x ) = 8 x ^ { 2 }f(x)=x+2;g(x)=8x2 Find (f - g)(x)

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)}f = \{ ( 9 , - 5 ) , ( 4,17 ) , ( - 18,11 ) \}f={(9,−5),(4,17),(−18,11)}

Use a calculator to approximate the natural logarithm to four decimal places. -ln 205

Find the exact value. - ln⁡e3\ln \mathrm { e } ^ { 3 }lne3

f(x)=x;g(x)=4x−1f ( x ) = \sqrt { x } ; g ( x ) = 4 x - 1f(x)=x​;g(x)=4x−1 Find (fg)(x)\left( \frac { f } { g } \right) ( x )(gf​)(x)

Determine whether the function is one-to-one. If it is one-to-one find an equation or a set of ordered pairs that defines the inverse function of the given function. - f(x)=5−4xf ( x ) = 5 - 4 xf(x)=5−4x

Find the value of the logarithmic expression. - log⁡648\log _ { 64 } 8log64​8

f(x)=−4x4;g(x)=−2x2f ( x ) = - 4 x ^ { 4 } ; g ( x ) = - 2 x ^ { 2 }f(x)=−4x4;g(x)=−2x2 Find (fg)(x).\left( \frac { f } { g } \right) ( x ) .(gf​)(x).

Find f(x) and g(x) so that the given function h(x) = (f ° g)(x). - h(x)=∣6−7x2∣h ( x ) = \left| 6 - 7 x ^ { 2 } \right|h(x)=​6−7x2​

Solve for x. - log⁡10x=1\log _ { 10 } x = 1log10​x=1

Solve the equation. - log⁡5x+log⁡5(x−24)=2\log _ { 5 } x + \log _ { 5 } ( x - 24 ) = 2log5​x+log5​(x−24)=2

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

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

Write as a logarithmic equation. - 23=82 ^ { 3 } = 823=8