Question 1

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

Accepted Answer

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

Question 2

Solve the equation without using a calculator.
-$3 ^ { x } = \frac { 1 } { 9 }$

Accepted Answer

A) 2 
B) -2 
C) 13 
D) 12 
A) 2 
B) -2 
C) 13 
D) 12 B

Question 3

Determine whether the given functions are inverses of each other.
-$$f ( x ) = \sqrt { x } , x \geq 0 , \quad g ( x ) = x ^ { 2 } , x \geq 0$$

Accepted Answer

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

Question 4

Find the value obtained when 10 is raised to the given exponent. Round to three significant digits.
--1.4375

Accepted Answer

A) 27.4 
B) -0.0365 
C) 0.0365 
D) -27.4 
A) 27.4 
B) -0.0365 
C) 0.0365 
D) -27.4

Question 5

A one-to-one function f is given. $\text { Find } \mathrm { f } ^ { - 1 } ( \mathrm { x } )$ and graph fwith a solid line and $f ^ { - 1 } ( x )$ with a dotted line on the same axes.
-$f ( x ) = \frac { 4 } { x } , x \geq 0$

Accepted Answer

A)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 4 } { \mathrm { x } } , \mathrm { x } \leq 0$
  
B)  $f ^ { - 1 } ( x ) = \frac { 4 } { x } , x \geq 0 ; f ( x ) = f ^ { - 1 } ( x )$
  
C)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = - \frac { 4 } { \mathrm { x } } , \mathrm { x } \geq 0$
  
D)  $f ^ { - 1 } ( x ) = - \frac { 4 } { x } , x \leq 0$
  
A)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 4 } { \mathrm { x } } , \mathrm { x } \leq 0$
  
B)  $f ^ { - 1 } ( x ) = \frac { 4 } { x } , x \geq 0 ; f ( x ) = f ^ { - 1 } ( x )$
  
C)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = - \frac { 4 } { \mathrm { x } } , \mathrm { x } \geq 0$
  
D)  $f ^ { - 1 } ( x ) = - \frac { 4 } { x } , x \leq 0$

Question 6

Solve the equation.
-$$\ln ( 14 ) - \ln x = \ln ( x - 5 )$$

Accepted Answer

A) 7 
B)  $\frac { 19 } { 2 }$ 
C) 7, -2 
D) -2 
A) 7 
B)  $\frac { 19 } { 2 }$ 
C) 7, -2 
D) -2

Question 7

Use properties of logarithms to expand the logarithmic expression as much as possible.
-$\log _ { e } y ^ { - z }$

Accepted Answer

A)  $- z \log _ { \mathrm { e } } \mathrm { y }$ 
B)  $- y \log _ { e } z$ 
C)  $y \log _ { e } z$ 
D)  $z \log _ { e } y$ 
A)  $- z \log _ { \mathrm { e } } \mathrm { y }$ 
B)  $- y \log _ { e } z$ 
C)  $y \log _ { e } z$ 
D)  $z \log _ { e } y$

Question 8

Solve the equation.
-$$\ln x + \ln ( x - 1 ) = \ln 2$$

Accepted Answer

A) 2, -1 
B) -1 
C)  $\frac { 3 } { 2 }$ 
D) 2 
A) 2, -1 
B) -1 
C)  $\frac { 3 } { 2 }$ 
D) 2

Question 9

A one-to-one function f is given. $\text { Find } \mathrm { f } ^ { - 1 } ( \mathrm { x } )$ and graph fwith a solid line and $f ^ { - 1 } ( x )$ with a dotted line on the same axes.
-$f ( x ) = x ^ { 3 } + 1$

Accepted Answer

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

Question 10

Evaluate.
-$$7 \log 10 ^ { 1.6 }$$

Accepted Answer

A) 11.2 
B) 1.12 
C) 3.2900 
D) 112 
A) 11.2 
B) 1.12 
C) 3.2900 
D) 112

Question 11

Find the antilog of the logarithm. Round the answer to six decimal places.
--1.4972

Accepted Answer

A) 4.469158 
B) 31.419553 
C) 0.708402 
D) 0.031827 
A) 4.469158 
B) 31.419553 
C) 0.708402 
D) 0.031827

Question 12

For the given functions f and g , find the indicated composition.
-$$\begin{array} { l } 
f ( x ) = \frac { x - 7 } { 10 } , \quad g ( x ) = 10 x + 7 \
( g \circ f ) ( x )
\end{array}$$

Accepted Answer

A)  $x - \frac { 7 } { 10 }$ 
B) 10x + 63 
C) x 
D) x + 14 
A)  $x - \frac { 7 } { 10 }$ 
B) 10x + 63 
C) x 
D) x + 14

Question 13

Determine whether the given function is one-to-one. If it is one-to-one, find its inverse function.
-$f ( x ) = x ^ { 2 } - 1 , x \geq 0$

Accepted Answer

A)  $f ^ { - 1 } ( x ) = \sqrt { x } + 1 , x \geq 0$ 
B)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt { \mathrm { x } + 1 } , \mathrm { x } \geq - 1$ 
C)  $f ^ { - 1 } ( x ) = \sqrt { x - 1 } , x \geq 1$ 
D) not a one-to-one function 
A)  $f ^ { - 1 } ( x ) = \sqrt { x } + 1 , x \geq 0$ 
B)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt { \mathrm { x } + 1 } , \mathrm { x } \geq - 1$ 
C)  $f ^ { - 1 } ( x ) = \sqrt { x - 1 } , x \geq 1$ 
D) not a one-to-one function

Question 14

Evaluate.
-$\log _ { 7 } \frac { 1 } { 343 }$

Accepted Answer

A) -3 
B) 49 
C) -49 
D) 3 
A) -3 
B) 49 
C) -49 
D) 3

Question 15

Solve the equation.
-$$\ln x = \frac { 3 } { 2 } \ln 64$$

Accepted Answer

A) 96 
B) 512 
C)  $\frac { 128 } { 3 }$ 
D) 2.7093 
A) 96 
B) 512 
C)  $\frac { 128 } { 3 }$ 
D) 2.7093

Question 16

Graph the function.
-$f ( x ) = 3 ^ { - x }$

Accepted Answer

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

Question 17

Solve the equation without using a calculator.
-$$3 ^ { - x } = \frac { 1 } { 9 }$$

Accepted Answer

A) 2 
B)  $\frac { 1 } { 3 }$ 
C)  $\frac { 1 } { 2 }$ 
D) -2 
A) 2 
B)  $\frac { 1 } { 3 }$ 
C)  $\frac { 1 } { 2 }$ 
D) -2

Question 18

Determine whether the function is a one-to-one function.
-$$y = ( x + 5 ) ^ { 3 }$$

Accepted Answer

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

Question 19

Solve for the indicated variable.
-$$P = 110 e ^ { 6 t } , \text { for } t$$

Accepted Answer

A)  $\mathrm { t } = \frac { \ln \mathrm { P } + \ln 110 } { 6 }$ 
B)  $t = \frac { \ln ( P - 110 ) } { 6 }$ 
C)  $t = \frac { P } { 110 e ^ { 6 } }$ 
D)  $t = \frac { \ln P - \ln 110 } { 6 }$ 
A)  $\mathrm { t } = \frac { \ln \mathrm { P } + \ln 110 } { 6 }$ 
B)  $t = \frac { \ln ( P - 110 ) } { 6 }$ 
C)  $t = \frac { P } { 110 e ^ { 6 } }$ 
D)  $t = \frac { \ln P - \ln 110 } { 6 }$

Question 20

Graph the function.
-$f ( x ) = 2 ^ { x } + 1$

Accepted Answer

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

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

Solve the equation without using a calculator. - $3 ^ { x } = \frac { 1 } { 9 }$

Determine whether the given functions are inverses of each other. - $f ( x ) = \sqrt { x } , x \geq 0 , \quad g ( x ) = x ^ { 2 } , x \geq 0$

Find the value obtained when 10 is raised to the given exponent. Round to three significant digits. --1.4375

Solve the equation. - $\ln ( 14 ) - \ln x = \ln ( x - 5 )$

Use properties of logarithms to expand the logarithmic expression as much as possible. - $\log _ { e } y ^ { - z }$

Solve the equation. - $\ln x + \ln ( x - 1 ) = \ln 2$

Evaluate. - $7 \log 10 ^ { 1.6 }$

Find the antilog of the logarithm. Round the answer to six decimal places. --1.4972

For the given functions f and g , find the indicated composition. - f(x)=,g(x)=10x+7 (g\circf)(x)

Determine whether the given function is one-to-one. If it is one-to-one, find its inverse function. - $f ( x ) = x ^ { 2 } - 1 , x \geq 0$

Evaluate. - $\log _ { 7 } \frac { 1 } { 343 }$

Solve the equation. - $\ln x = \frac { 3 } { 2 } \ln 64$

Graph the function. - $f ( x ) = 3 ^ { - x }$ $Graph the function. - f ( x ) = 3 ^ { - x }$

Solve the equation without using a calculator. - $3 ^ { - x } = \frac { 1 } { 9 }$

Determine whether the function is a one-to-one function. - $y = ( x + 5 ) ^ { 3 }$

Solve for the indicated variable. - $P = 110 e ^ { 6 t } , \text { for } t$

Graph the function. - $f ( x ) = 2 ^ { x } + 1$ $Graph the function. - f ( x ) = 2 ^ { x } + 1$

Basic Concepts

Equations and Inequalities

Graphs and Functions

Systems of Equations and Inequalities

Polynomials and Polynomial Functions

Rational Expressions and Equations

Roots, Radicals, and Complex Numbers

Quadratic Functions

Characteristics of Functions and Their Graphs

Conic Sections

Sequences, Series, and Probability

Filters

Exam 9: Exponential and Logarithmic Functions

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

Solve the equation without using a calculator. - 3x=193 ^ { x } = \frac { 1 } { 9 }3x=91​

Determine whether the given functions are inverses of each other. - f(x)=x,x≥0,g(x)=x2,x≥0f ( x ) = \sqrt { x } , x \geq 0 , \quad g ( x ) = x ^ { 2 } , x \geq 0f(x)=x​,x≥0,g(x)=x2,x≥0

Find the value obtained when 10 is raised to the given exponent. Round to three significant digits. --1.4375

A one-to-one function f is given. Find f−1(x)\text { Find } \mathrm { f } ^ { - 1 } ( \mathrm { x } ) Find f−1(x) and graph fwith a solid line and f−1(x)f ^ { - 1 } ( x )f−1(x) with a dotted line on the same axes. - f(x)=4x,x≥0f ( x ) = \frac { 4 } { x } , x \geq 0f(x)=x4​,x≥0

Solve the equation. - ln⁡(14)−ln⁡x=ln⁡(x−5)\ln ( 14 ) - \ln x = \ln ( x - 5 )ln(14)−lnx=ln(x−5)

Use properties of logarithms to expand the logarithmic expression as much as possible. - log⁡ey−z\log _ { e } y ^ { - z }loge​y−z

Solve the equation. - ln⁡x+ln⁡(x−1)=ln⁡2\ln x + \ln ( x - 1 ) = \ln 2lnx+ln(x−1)=ln2

A one-to-one function f is given. Find f−1(x)\text { Find } \mathrm { f } ^ { - 1 } ( \mathrm { x } ) Find f−1(x) and graph fwith a solid line and f−1(x)f ^ { - 1 } ( x )f−1(x) with a dotted line on the same axes. - f(x)=x3+1f ( x ) = x ^ { 3 } + 1f(x)=x3+1

Evaluate. - 7log⁡101.67 \log 10 ^ { 1.6 }7log101.6