Question 1

If the function is one-to-one, find its inverse. If not, write ʺnot one-to-one.ʺ
-$$\{ ( - 11,9 ) , ( 4,9 ) , ( - 14,18 ) \}$$

Accepted Answer

A)  $\{ ( 9 , - 11 ) , ( - 14,4 ) , ( 18,9 ) \}$ 
B)  not one-to-one 
C)  $\{ ( 9 , - 11 ) , ( 9,4 ) , ( 18 , - 14 ) \}$ 
D)  $\{ ( - 11,9 ) , ( 9,4 ) , ( 18 , - 14 ) \}$ 
A)  $\{ ( 9 , - 11 ) , ( - 14,4 ) , ( 18,9 ) \}$ 
B)  not one-to-one 
C)  $\{ ( 9 , - 11 ) , ( 9,4 ) , ( 18 , - 14 ) \}$ 
D)  $\{ ( - 11,9 ) , ( 9,4 ) , ( 18 , - 14 ) \}$

Question 2

Determine whether or not the function is one-to-one.
-$$f ( x ) = \frac { - 9 x - 5 } { 7 x + 4 }$$

Accepted Answer

A)  No 
B)  Yes 
A)  No 
B)  Yes

Question 3

Solve the problem.
-If $f ( x ) = \log _ { 3 } x$, find $f \left( 3 ^ { 3 \log _ { 3 } 3 } \right)$.

Accepted Answer

A)  0 
B)  1 
C)  9 
D)  3 
A)  0 
B)  1 
C)  9 
D)  3

Question 4

Solve the equation.
-$$\left( \frac { 1 } { 3 } \right) ^ { 4 x + 3 } = 9 ^{x - 5}$$

Accepted Answer

A)  $\left\{ \frac { 13 } { 4 } \right\}$ 
B)  $\left\{ \frac { 2 } { 5 } \right\}$ 
C)  $\left\{ \frac { 7 } { 6 } \right\}$ 
D)  $\left\{ \frac { 1 } { 3 } \right\}$ 
A)  $\left\{ \frac { 13 } { 4 } \right\}$ 
B)  $\left\{ \frac { 2 } { 5 } \right\}$ 
C)  $\left\{ \frac { 7 } { 6 } \right\}$ 
D)  $\left\{ \frac { 1 } { 3 } \right\}$

Question 5

Solve the equation. Round to the nearest thousandth.
-$2 \mathrm { e } ^ { ( 5 \mathrm { x } + 3 ) } = 8$

Accepted Answer

A)  $\{ 0.877 \}$ 
B)  $\{ 1.000 \}$ 
C)  $\{ - 0.392 \}$ 
D)  $\{ - 0.323 \}$ 
A)  $\{ 0.877 \}$ 
B)  $\{ 1.000 \}$ 
C)  $\{ - 0.392 \}$ 
D)  $\{ - 0.323 \}$

Question 6

Decide whether or not the functions are inverses of each other.Use the definition of inverses to determine whether f and g are inverses.
-$$f ( x ) = 8 x - 8 , \quad g ( x ) = \frac { 1 } { 8 } x + 1$$

Accepted Answer

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

Question 7

Provide an appropriate response.
-Use the properties of exponents to write the function of the form $f ( t ) = k a^ t$, where $k$ is a constant. $f ( t ) = \left( \frac { 1 } { 3 } \right) ^ { 2 - 3 t }$

Accepted Answer

A)  $f ( t ) = \frac { 1 } { 9 } \left( \frac { 1 } { 27 } \right)^ t$ 
B)  $f ( t ) = \left( \frac { 1 } { 27 } \right) 9^ t$ 
C)  $f ( t ) = 9 \cdot 27 ^t$ 
D)  $f ( t ) = \left( \frac { 1 } { 9 } \right) 27 ^t$ 
A)  $f ( t ) = \frac { 1 } { 9 } \left( \frac { 1 } { 27 } \right)^ t$ 
B)  $f ( t ) = \left( \frac { 1 } { 27 } \right) 9^ t$ 
C)  $f ( t ) = 9 \cdot 27 ^t$ 
D)  $f ( t ) = \left( \frac { 1 } { 9 } \right) 27 ^t$

Question 8

Solve the equation and express the solution in exact form.
-$\log 2 x = \log 3 + \log ( x - 4 )$

Accepted Answer

A)  $\{ 12 \}$ 
B)  $\{ 4 \}$ 
C)  $\left\{ - \frac { 12 } { 5 } \right\}$ 
D)  $\{ - 1 \}$ 
A)  $\{ 12 \}$ 
B)  $\{ 4 \}$ 
C)  $\left\{ - \frac { 12 } { 5 } \right\}$ 
D)  $\{ - 1 \}$

Question 9

Find the future value.
-$4232 invested for 4 years at 6% compounded annually

Accepted Answer

A)  $5376.71 
B)  $5360.97 
C)  $5370.35 
D)  $5342.80 
A)  $5376.71 
B)  $5360.97 
C)  $5370.35 
D)  $5342.80

Question 10

Use the graph of f to sketch a graph of the inverse of f using a dashed curve.
-

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 11

Graph the function. Give the domain and range.
-$f(x)=\log _{1 / 6}{ }^{x}$

Accepted Answer

A)  domain: $( 0 , \infty )$; range: $( - \infty , \infty )$
  
B)  domain: $( 0 , \infty ) ;$ range: $( - \infty , \infty )$
  
C)  domain: $( - \infty , \infty )$; range: $( - \infty , 0 )$
  
D)  domain: $( - \infty , \infty )$; range: $( 0 , \infty )$
  
A)  domain: $( 0 , \infty )$; range: $( - \infty , \infty )$
  
B)  domain: $( 0 , \infty ) ;$ range: $( - \infty , \infty )$
  
C)  domain: $( - \infty , \infty )$; range: $( - \infty , 0 )$
  
D)  domain: $( - \infty , \infty )$; range: $( 0 , \infty )$

Question 12

Solve the equation.
-$$4 ( 7 + 3 x ) = \frac { 1 } { 16 }$$

Accepted Answer

A)  $\left\{ \frac { 1 } { 4 } \right\}$ 
B)  $\{ 3 \}$ 
C)  $\{ 4 \}$ 
D)  $\{ - 3 \}$ 
A)  $\left\{ \frac { 1 } { 4 } \right\}$ 
B)  $\{ 3 \}$ 
C)  $\{ 4 \}$ 
D)  $\{ - 3 \}$

Question 13

Solve the problem.
-Let $u = \ln a$ and $v = \ln b$. Write the following expression in terms of $u$ and $v$ without using the function $\ln$.
$\ln \sqrt [ 3 ] { \frac { a ^ { 6 } } { b ^ { 9 } } }$

Accepted Answer

A)  $18 u - 27 v$ 
B)  $6 u - 9 v$ 
C)  $2 u - 3 v$ 
D)  $18 u + 27 v$ 
A)  $18 u - 27 v$ 
B)  $6 u - 9 v$ 
C)  $2 u - 3 v$ 
D)  $18 u + 27 v$

Question 14

Find the value. Give an approximation to four decimal places.
-$\log 0.00542$

Accepted Answer

A)  $- 2.2741$ 
B)  $- 2.2660$ 
C)  $- 5.2177$ 
D)  $- 2.2581$ 
A)  $- 2.2741$ 
B)  $- 2.2660$ 
C)  $- 5.2177$ 
D)  $- 2.2581$

Question 15

If the function is one-to-one, find its inverse. If not, write ʺnot one-to-one.ʺ
-$$\{ ( 3 , - 5 ) , ( 5 , - 3 ) , ( 9,2 ) , ( - 9 , - 2 ) \}$$

Accepted Answer

A)  $\{ ( - 2,9 ) , ( 9,5 ) , ( - 5,3 ) , ( 2 , - 9 ) \}$ 
B)  $\{ ( - 5,3 ) , ( - 3,5 ) , ( 2,9 ) , ( - 2 , - 9 ) \}$ 
C)  $\{ ( - 2,9 ) , ( - 3,5 ) , ( - 5,5 ) , ( 2 , - 9 ) \}$ 
D)  not one-to-one 
A)  $\{ ( - 2,9 ) , ( 9,5 ) , ( - 5,3 ) , ( 2 , - 9 ) \}$ 
B)  $\{ ( - 5,3 ) , ( - 3,5 ) , ( 2,9 ) , ( - 2 , - 9 ) \}$ 
C)  $\{ ( - 2,9 ) , ( - 3,5 ) , ( - 5,5 ) , ( 2 , - 9 ) \}$ 
D)  not one-to-one

Question 16

Use the graph of f to sketch a graph of the inverse of f using a dashed curve.
-

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 17

Decide whether the given functions are inverses.
-

Accepted Answer

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

Question 18

Solve the equation and express the solution in exact form.
-$$\log _ { 3 } \left( \log _ { 3 } x \right) = 1$$

Accepted Answer

A)  $\{ 27 \}$ 
B)  $\{ 6 \}$ 
C)  $\{ 9 \}$ 
D)  $\{ 3 \}$ 
A)  $\{ 27 \}$ 
B)  $\{ 6 \}$ 
C)  $\{ 9 \}$ 
D)  $\{ 3 \}$

Question 19

Solve the equation and express the solution in exact form.
-$\ln 9 x + \ln 7 x = \ln 64$

Accepted Answer

A)  $\left\{ \frac { e ^ { 64 } } { 63 } \right\}$ 
B)  $\{ 1 \}$ 
C)  $\{ 0 \}$ 
D)  $\left\{ \left( \frac { 64 } { 63 } \right) ^ { 1 / 2 } \right\}$ 
A)  $\left\{ \frac { e ^ { 64 } } { 63 } \right\}$ 
B)  $\{ 1 \}$ 
C)  $\{ 0 \}$ 
D)  $\left\{ \left( \frac { 64 } { 63 } \right) ^ { 1 / 2 } \right\}$

Question 20

If the function is one-to-one, find its inverse. If not, write ʺnot one-to-one.ʺ
-$$\{ ( - 19 , - 4 ) , ( 7 , - 12 ) , ( 16 , - 1 ) \}$$

Accepted Answer

A)  $\{ ( - 19 , - 12 ) , ( - 19,7 ) , ( - 1,16 ) \}$ 
B)  $\{ ( - 4 , - 19 ) , ( - 12,7 ) , ( - 1,16 ) \}$ 
C)  $\{ ( - 4 , - 19 ) , ( 16,7 ) , ( - 1 , - 12 ) \}$ 
D)  not one-to-one 
A)  $\{ ( - 19 , - 12 ) , ( - 19,7 ) , ( - 1,16 ) \}$ 
B)  $\{ ( - 4 , - 19 ) , ( - 12,7 ) , ( - 1,16 ) \}$ 
C)  $\{ ( - 4 , - 19 ) , ( 16,7 ) , ( - 1 , - 12 ) \}$ 
D)  not one-to-one

If the function is one-to-one, find its inverse. If not, write ʺnot one-to-one.ʺ - $\{ ( - 11,9 ) , ( 4,9 ) , ( - 14,18 ) \}$

Determine whether or not the function is one-to-one. - $f ( x ) = \frac { - 9 x - 5 } { 7 x + 4 }$

Solve the problem. -If $f ( x ) = \log _ { 3 } x$ , find $f \left( 3 ^ { 3 \log _ { 3 } 3 } \right)$ .

Solve the equation. - $\left( \frac { 1 } { 3 } \right) ^ { 4 x + 3 } = 9 ^{x - 5}$

Solve the equation. Round to the nearest thousandth. - $2 \mathrm { e } ^ { ( 5 \mathrm { x } + 3 ) } = 8$

Decide whether or not the functions are inverses of each other.Use the definition of inverses to determine whether f and g are inverses. - $f ( x ) = 8 x - 8 , \quad g ( x ) = \frac { 1 } { 8 } x + 1$

Provide an appropriate response. -Use the properties of exponents to write the function of the form $f ( t ) = k a^ t$ , where $k$ is a constant. $f ( t ) = \left( \frac { 1 } { 3 } \right) ^ { 2 - 3 t }$

Solve the equation and express the solution in exact form. - $\log 2 x = \log 3 + \log ( x - 4 )$

Find the future value. -$4232 invested for 4 years at 6% compounded annually

Use the graph of f to sketch a graph of the inverse of f using a dashed curve. -

Graph the function. Give the domain and range. - $f(x)=\log _{1 / 6}{ }^{x}$ $Graph the function. Give the domain and range. - f(x)=\log _{1 / 6}{ }^{x}$

Solve the equation. - $4 ( 7 + 3 x ) = \frac { 1 } { 16 }$

Solve the problem. -Let $u = \ln a$ and $v = \ln b$ . Write the following expression in terms of $u$ and $v$ without using the function $\ln$ . $\ln \sqrt [ 3 ] { \frac { a ^ { 6 } } { b ^ { 9 } } }$

Find the value. Give an approximation to four decimal places. - $\log 0.00542$

If the function is one-to-one, find its inverse. If not, write ʺnot one-to-one.ʺ - $\{ ( 3 , - 5 ) , ( 5 , - 3 ) , ( 9,2 ) , ( - 9 , - 2 ) \}$

Use the graph of f to sketch a graph of the inverse of f using a dashed curve. -

Decide whether the given functions are inverses. -

Solve the equation and express the solution in exact form. - $\log _ { 3 } \left( \log _ { 3 } x \right) = 1$

Solve the equation and express the solution in exact form. - $\ln 9 x + \ln 7 x = \ln 64$

If the function is one-to-one, find its inverse. If not, write ʺnot one-to-one.ʺ - $\{ ( - 19 , - 4 ) , ( 7 , - 12 ) , ( 16 , - 1 ) \}$

Equations and Inequalities

Graphs and Functions

Polynomial and Rational Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Analytic Geometry

Further Topics in Algebra

Review of Basic Concepts

Filters

Exam 4: Inverse, Exponential, and Logarithmic Functions

If the function is one-to-one, find its inverse. If not, write ʺnot one-to-one.ʺ - {(−11,9),(4,9),(−14,18)}\{ ( - 11,9 ) , ( 4,9 ) , ( - 14,18 ) \}{(−11,9),(4,9),(−14,18)}

Determine whether or not the function is one-to-one. - f(x)=−9x−57x+4f ( x ) = \frac { - 9 x - 5 } { 7 x + 4 }f(x)=7x+4−9x−5​

Solve the problem. -If f(x)=log⁡3xf ( x ) = \log _ { 3 } xf(x)=log3​x , find f(33log⁡33)f \left( 3 ^ { 3 \log _ { 3 } 3 } \right)f(33log3​3) .

Solve the equation. - (13)4x+3=9x−5\left( \frac { 1 } { 3 } \right) ^ { 4 x + 3 } = 9 ^{x - 5}(31​)4x+3=9x−5

Solve the equation. Round to the nearest thousandth. - 2e(5x+3)=82 \mathrm { e } ^ { ( 5 \mathrm { x } + 3 ) } = 82e(5x+3)=8

Decide whether or not the functions are inverses of each other.Use the definition of inverses to determine whether f and g are inverses. - f(x)=8x−8,g(x)=18x+1f ( x ) = 8 x - 8 , \quad g ( x ) = \frac { 1 } { 8 } x + 1f(x)=8x−8,g(x)=81​x+1

Provide an appropriate response. -Use the properties of exponents to write the function of the form f(t)=katf ( t ) = k a^ tf(t)=kat , where kkk is a constant. f(t)=(13)2−3tf ( t ) = \left( \frac { 1 } { 3 } \right) ^ { 2 - 3 t }f(t)=(31​)2−3t

Solve the equation and express the solution in exact form. - log⁡2x=log⁡3+log⁡(x−4)\log 2 x = \log 3 + \log ( x - 4 )log2x=log3+log(x−4)

Find the future value. -$4232 invested for 4 years at 6% compounded annually

Use the graph of f to sketch a graph of the inverse of f using a dashed curve. -

Graph the function. Give the domain and range. - f(x)=log⁡1/6xf(x)=\log _{1 / 6}{ }^{x}f(x)=log1/6​x

Solve the equation. - 4(7+3x)=1164 ( 7 + 3 x ) = \frac { 1 } { 16 }4(7+3x)=161​

Solve the problem. -Let u=ln⁡au = \ln au=lna and v=ln⁡bv = \ln bv=lnb . Write the following expression in terms of uuu and vvv without using the function ln⁡\lnln . ln⁡a6b93\ln \sqrt [ 3 ] { \frac { a ^ { 6 } } { b ^ { 9 } } }ln3b9a6​​

Find the value. Give an approximation to four decimal places. - log⁡0.00542\log 0.00542log0.00542

If the function is one-to-one, find its inverse. If not, write ʺnot one-to-one.ʺ - {(3,−5),(5,−3),(9,2),(−9,−2)}\{ ( 3 , - 5 ) , ( 5 , - 3 ) , ( 9,2 ) , ( - 9 , - 2 ) \}{(3,−5),(5,−3),(9,2),(−9,−2)}

Use the graph of f to sketch a graph of the inverse of f using a dashed curve. -

Decide whether the given functions are inverses. -

Solve the equation and express the solution in exact form. - log⁡3(log⁡3x)=1\log _ { 3 } \left( \log _ { 3 } x \right) = 1log3​(log3​x)=1

Solve the equation and express the solution in exact form. - ln⁡9x+ln⁡7x=ln⁡64\ln 9 x + \ln 7 x = \ln 64ln9x+ln7x=ln64

If the function is one-to-one, find its inverse. If not, write ʺnot one-to-one.ʺ - {(−19,−4),(7,−12),(16,−1)}\{ ( - 19 , - 4 ) , ( 7 , - 12 ) , ( 16 , - 1 ) \}{(−19,−4),(7,−12),(16,−1)}

Equations and Inequalities

Graphs and Functions

Polynomial and Rational Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Analytic Geometry

Further Topics in Algebra

Review of Basic Concepts

Filters

If the function is one-to-one, find its inverse. If not, write ʺnot one-to-one.ʺ - $\{ ( - 11,9 ) , ( 4,9 ) , ( - 14,18 ) \}$

Determine whether or not the function is one-to-one. - $f ( x ) = \frac { - 9 x - 5 } { 7 x + 4 }$

Solve the problem. -If $f ( x ) = \log _ { 3 } x$ , find $f \left( 3 ^ { 3 \log _ { 3 } 3 } \right)$ .

Solve the equation. - $\left( \frac { 1 } { 3 } \right) ^ { 4 x + 3 } = 9 ^{x - 5}$

Solve the equation. Round to the nearest thousandth. - $2 \mathrm { e } ^ { ( 5 \mathrm { x } + 3 ) } = 8$

Decide whether or not the functions are inverses of each other.Use the definition of inverses to determine whether f and g are inverses. - $f ( x ) = 8 x - 8 , \quad g ( x ) = \frac { 1 } { 8 } x + 1$

Provide an appropriate response. -Use the properties of exponents to write the function of the form $f ( t ) = k a^ t$ , where $k$ is a constant. $f ( t ) = \left( \frac { 1 } { 3 } \right) ^ { 2 - 3 t }$

Solve the equation and express the solution in exact form. - $\log 2 x = \log 3 + \log ( x - 4 )$

Graph the function. Give the domain and range. - $f(x)=\log _{1 / 6}{ }^{x}$ $Graph the function. Give the domain and range. - f(x)=\log _{1 / 6}{ }^{x}$

Solve the equation. - $4 ( 7 + 3 x ) = \frac { 1 } { 16 }$

Solve the problem. -Let $u = \ln a$ and $v = \ln b$ . Write the following expression in terms of $u$ and $v$ without using the function $\ln$ . $\ln \sqrt [ 3 ] { \frac { a ^ { 6 } } { b ^ { 9 } } }$

Find the value. Give an approximation to four decimal places. - $\log 0.00542$

If the function is one-to-one, find its inverse. If not, write ʺnot one-to-one.ʺ - $\{ ( 3 , - 5 ) , ( 5 , - 3 ) , ( 9,2 ) , ( - 9 , - 2 ) \}$

Solve the equation and express the solution in exact form. - $\log _ { 3 } \left( \log _ { 3 } x \right) = 1$

Solve the equation and express the solution in exact form. - $\ln 9 x + \ln 7 x = \ln 64$

If the function is one-to-one, find its inverse. If not, write ʺnot one-to-one.ʺ - $\{ ( - 19 , - 4 ) , ( 7 , - 12 ) , ( 16 , - 1 ) \}$