Question 1

Write an equation of the inverse for the one-to-one function $$f ( x ) = 5 x ^ { 3 } - 5$$

Accepted Answer

A)  $f ^ { - 1 } ( x ) = \sqrt [ 3 ] { \frac { x + 5 } { 5 } }$ 
B)  $f ^ { - 1 } ( x ) = \left( \frac { x + 5 } { 5 } \right) ^ { 3 }$ 
C)  $f ^ { - 1 } ( x ) = \frac { x - 5 } { 5 }$ 
D)  $f ^ { - 1 } ( x ) = \frac { x + 5 } { 5 }$ 
A)  $f ^ { - 1 } ( x ) = \sqrt [ 3 ] { \frac { x + 5 } { 5 } }$ 
B)  $f ^ { - 1 } ( x ) = \left( \frac { x + 5 } { 5 } \right) ^ { 3 }$ 
C)  $f ^ { - 1 } ( x ) = \frac { x - 5 } { 5 }$ 
D)  $f ^ { - 1 } ( x ) = \frac { x + 5 } { 5 }$

Question 2

Graph y = f (x). $$f ( x ) = \log _ { 4 } x$$

Accepted Answer

The answer of Graph y = f (x). \[f (...

Question 3

Solve the logarithmic equation. $$\log _ { 9 } k + \log _ { 9 } ( 2 k + 9 ) = 2$$

Accepted Answer

A)  $\left\{ \frac { 9 } { 2 } \right\}$ 
B) {  } 
C)  $\left\{ - 9 , \frac { 9 } { 2 } \right\}$ 
D)  $\{ - 9 \}$ 
A)  $\left\{ \frac { 9 } { 2 } \right\}$ 
B) {  } 
C)  $\left\{ - 9 , \frac { 9 } { 2 } \right\}$ 
D)  $\{ - 9 \}$

Question 4

Write the expression as a single logarithm. Assume all variables represent positive real numbers. $$\log _ { b } x - \log _ { b } x ^ { 6 } + \log _ { b } x ^ { 8 }$$

Accepted Answer

A)  $\log _ { b } 3 x$ 
B)  $\log _ { b } x ^ { 2 }$ 
C)  $\log _ { b } 2 x$ 
D)  $\log _ { b } x ^ { 3 }$ 
A)  $\log _ { b } 3 x$ 
B)  $\log _ { b } x ^ { 2 }$ 
C)  $\log _ { b } 2 x$ 
D)  $\log _ { b } x ^ { 3 }$

Question 5

When money is invested at an interest rate of 4%, the value of the investment after t years is given by $A = P ( 1.04 ) ^ { t }$ where P is the original investment. If $24,000 is invested, how long would it take to reach a value of $36,000? Round to the nearest tenth of a year.

Accepted Answer

A)  5.7 years 
B)  2.3 years 
C)  10.3 years 
D)  21 years 
A)  5.7 years 
B)  2.3 years 
C)  10.3 years 
D)  21 years

Question 6

Write an equation of the inverse for the one-to-one function f (x) = 2x - 9.

Accepted Answer

A)  $f ^ { - 1 } ( x ) = \frac { 1 } { 2 x - 9 }$ 
B)  $f ^ { - 1 } ( x ) = \frac { x - 9 } { 2 }$ 
C)  $f ^ { - 1 } ( x ) = \frac { x + 9 } { 2 }$ 
D)  $f ^ { - 1 } ( x ) = \frac { 9 } { x } - 2$ 
A)  $f ^ { - 1 } ( x ) = \frac { 1 } { 2 x - 9 }$ 
B)  $f ^ { - 1 } ( x ) = \frac { x - 9 } { 2 }$ 
C)  $f ^ { - 1 } ( x ) = \frac { x + 9 } { 2 }$ 
D)  $f ^ { - 1 } ( x ) = \frac { 9 } { x } - 2$

Question 7

Solve the exponential equation by using the property that $b ^ { x } = b ^ { y } \text { implies } x = y \text {, for } b > 0 \text { and } b \neq 1 \text {. }$ 
$6.8 ^ { x - 3 } = 6.8 ^ { 2 x + 21 }$

Accepted Answer

A)  $\left\{ 6.8 ^ { - 24 } \right\}$ 
B)  {   } 
C)  $\{ 9 \}$ 
D)  $\{ - 24 \}$ 
A)  $\left\{ 6.8 ^ { - 24 } \right\}$ 
B)  {   } 
C)  $\{ 9 \}$ 
D)  $\{ - 24 \}$

Question 8

Carbon dating determines the approximate age of an object made from materials that wereonce alive by measuring the remaining percentage of a radioactive isotope, carbon-14. The age is calculated Using the formula $A = - \frac { \ln P } { 0.000121 }$ where P is the percentage of remaining carbon-14 (in decimal form). A specimen is determined to Be 3800 years old. What is the percentage of remaining carbon-14? Round to the nearest tenth of a Percent.

Accepted Answer

A)  23.1% 
B)  43.1% 
C)  76.1% 
D)  63.1% 
A)  23.1% 
B)  43.1% 
C)  76.1% 
D)  63.1%

Question 9

Solve the logarithmic equation. $\log ( x + - 2 ) = \log ( 2 x - 6 )$

Accepted Answer

A)  $\{ 10 \}$ 
B)  {  } 
C)  $\{ 4 \}$ 
D)  $\{ 4,10 \}$ 
A)  $\{ 10 \}$ 
B)  {  } 
C)  $\{ 4 \}$ 
D)  $\{ 4,10 \}$

Question 10

Verify that f and g are inverse functions by showing that $\text { (a) } ( f \circ g ) ( x ) = x \text { and(b) } ( g \circ f ) ( x ) = x \text {. }$ $$f ( x ) = x ^ { 3 } + 6 \text { and } g ( x ) = \sqrt [ 3 ] { x - 6 }$$

Accepted Answer

The answer of Verify that f and g are inverse...

Question 11

Solve the logarithmic equation. $$6 = 4 - \log _ { 2 } ( 2 x + 4 )$$

Accepted Answer

The answer of Solve the logarithmic equation. \[6 = 4...

Question 12

Solve the logarithmic equation. $$\log _ { 9 } ( 5 x + 7 ) - \log _ { 9 } x = \log _ { 9 } 6$$

Accepted Answer

A)  $\left\{ - \frac { 7 } { 11 } \right\}$ 
B)  $\left\{ \frac { 7 } { 11 } \right\}$ 
C) {  } 
D)  $\{ 7 \}$ 
A)  $\left\{ - \frac { 7 } { 11 } \right\}$ 
B)  $\left\{ \frac { 7 } { 11 } \right\}$ 
C) {  } 
D)  $\{ 7 \}$

Question 13

If $f ( x ) = 10 x + 7$ and $g ( x ) = x ^ { 2 } - 7 x$, find $( f - g ) ( x )$.

Accepted Answer

A)  $( f - g ) ( x ) = 10 x ^ { 2 } - 70 x + 7$ 
B)  $( f - g ) ( x ) = 10 x ^ { 3 } - 63 x ^ { 2 } - 49 x$ 
C)  $( f - g ) ( x ) = - x ^ { 2 } + 17 x + 7$ 
D)  $( f - g ) ( x ) = x ^ { 2 } + 3 x + 7$ 
A)  $( f - g ) ( x ) = 10 x ^ { 2 } - 70 x + 7$ 
B)  $( f - g ) ( x ) = 10 x ^ { 3 } - 63 x ^ { 2 } - 49 x$ 
C)  $( f - g ) ( x ) = - x ^ { 2 } + 17 x + 7$ 
D)  $( f - g ) ( x ) = x ^ { 2 } + 3 x + 7$

Question 14

Find the domain of the function and express the domain in interval notation. $$g ( x ) = \log \left( x ^ { 2 } + 8 \right)$$

Accepted Answer

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

Question 15

Find the domain of the function and express the domain in interval notation. $$f ( x ) = \log ( 5 x + 5 )$$

Accepted Answer

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

Question 16

Graph the equation by completing the table and plotting points. Round to two decimal places when necessary. $f(x)=e^{x-2}$
$\begin{array}{l|l}
x & y \
\hline 0 & \
\hline 2 & \
\hline 3 & \
\hline 4 &
\end{array}$

Accepted Answer

\[\begin{array} { l | l } 
x &

Question 17

Approximate the function value from the graph. $(f+g)(0)$

Accepted Answer

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

Question 18

$f ( x ) = \sqrt { x } \text { and } g ( x ) = \sqrt { x }$ are inverse functions because $f ( x ) \cdot g ( x ) = x$

Accepted Answer

A) True 
 B)False

Question 19

Evaluate without the use of a calculator. $$\log _ { 8 } \sqrt [ 5 ] { 8 }$$

Accepted Answer

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

Question 20

Use a calculator to approximate the logarithm. Round to 4 decimal places. $\log \left( 7.04 \times 10 ^ { 9 } \right)$

Accepted Answer

A)  $9.8476$ 
B)  $22.6749$ 
C)  $6.4514$ 
D)  $2.8018$ 
A)  $9.8476$ 
B)  $22.6749$ 
C)  $6.4514$ 
D)  $2.8018$

Write an equation of the inverse for the one-to-one function $f ( x ) = 5 x ^ { 3 } - 5$

Graph y = f (x). $f ( x ) = \log _ { 4 } x$

Solve the logarithmic equation. $\log _ { 9 } k + \log _ { 9 } ( 2 k + 9 ) = 2$

Write the expression as a single logarithm. Assume all variables represent positive real numbers. $\log _ { b } x - \log _ { b } x ^ { 6 } + \log _ { b } x ^ { 8 }$

When money is invested at an interest rate of 4%, the value of the investment after t years is given by $A = P ( 1.04 ) ^ { t }$ where P is the original investment. If $24,000 is invested, how long would it take to reach a value of $36,000? Round to the nearest tenth of a year.

Write an equation of the inverse for the one-to-one function f (x) = 2x - 9.

Solve the exponential equation by using the property that $b ^ { x } = b ^ { y } \text { implies } x = y \text {, for } b > 0 \text { and } b \neq 1 \text {. }$ $6.8 ^ { x - 3 } = 6.8 ^ { 2 x + 21 }$

Solve the logarithmic equation. $\log ( x + - 2 ) = \log ( 2 x - 6 )$

Verify that f and g are inverse functions by showing that $\text { (a) } ( f \circ g ) ( x ) = x \text { and(b) } ( g \circ f ) ( x ) = x \text {. }$ $f ( x ) = x ^ { 3 } + 6 \text { and } g ( x ) = \sqrt [ 3 ] { x - 6 }$

Solve the logarithmic equation. $6 = 4 - \log _ { 2 } ( 2 x + 4 )$

Solve the logarithmic equation. $\log _ { 9 } ( 5 x + 7 ) - \log _ { 9 } x = \log _ { 9 } 6$

If $f ( x ) = 10 x + 7$ and $g ( x ) = x ^ { 2 } - 7 x$ , find $( f - g ) ( x )$ .

Find the domain of the function and express the domain in interval notation. $g ( x ) = \log \left( x ^ { 2 } + 8 \right)$

Find the domain of the function and express the domain in interval notation. $f ( x ) = \log ( 5 x + 5 )$

Graph the equation by completing the table and plotting points. Round to two decimal places when necessary. $f(x)=e^{x-2}$ x y 0 2 3 4

Approximate the function value from the graph. $(f+g)(0)$

$f ( x ) = \sqrt { x } \text { and } g ( x ) = \sqrt { x }$ are inverse functions because $f ( x ) \cdot g ( x ) = x$

Evaluate without the use of a calculator. $\log _ { 8 } \sqrt [ 5 ] { 8 }$

Use a calculator to approximate the logarithm. Round to 4 decimal places. $\log \left( 7.04 \times 10 ^ { 9 } \right)$

Linear Equations and Inequalities in One Variable

Linear Equations in Two Variables and Functions

Systems of Linear Equations and Inequalities

Polynomials

Rational Expressions and Rational Equations

Radicals and Complex Numbers

Quadratic Equations, Functions and Inequalities

Conic Sections

Binomial Expansions, Sequences, and Series

Online: Transformations, Piecewise-Defined Functions, and Probability

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Exam 8: Exponential and Logarithmic Functions and Applications

Write an equation of the inverse for the one-to-one function f(x)=5x3−5f ( x ) = 5 x ^ { 3 } - 5f(x)=5x3−5

Graph y = f (x). f(x)=log⁡4xf ( x ) = \log _ { 4 } xf(x)=log4​x

Solve the logarithmic equation. log⁡9k+log⁡9(2k+9)=2\log _ { 9 } k + \log _ { 9 } ( 2 k + 9 ) = 2log9​k+log9​(2k+9)=2

Write the expression as a single logarithm. Assume all variables represent positive real numbers. log⁡bx−log⁡bx6+log⁡bx8\log _ { b } x - \log _ { b } x ^ { 6 } + \log _ { b } x ^ { 8 }logb​x−logb​x6+logb​x8

When money is invested at an interest rate of 4%, the value of the investment after t years is given by A=P(1.04)tA = P ( 1.04 ) ^ { t }A=P(1.04)t where P is the original investment. If $24,000 is invested, how long would it take to reach a value of $36,000? Round to the nearest tenth of a year.

Write an equation of the inverse for the one-to-one function f (x) = 2x - 9.

Solve the logarithmic equation. log⁡(x+−2)=log⁡(2x−6)\log ( x + - 2 ) = \log ( 2 x - 6 )log(x+−2)=log(2x−6)

Solve the logarithmic equation. 6=4−log⁡2(2x+4)6 = 4 - \log _ { 2 } ( 2 x + 4 )6=4−log2​(2x+4)

Solve the logarithmic equation. log⁡9(5x+7)−log⁡9x=log⁡96\log _ { 9 } ( 5 x + 7 ) - \log _ { 9 } x = \log _ { 9 } 6log9​(5x+7)−log9​x=log9​6

If f(x)=10x+7f ( x ) = 10 x + 7f(x)=10x+7 and g(x)=x2−7xg ( x ) = x ^ { 2 } - 7 xg(x)=x2−7x , find (f−g)(x)( f - g ) ( x )(f−g)(x) .

Find the domain of the function and express the domain in interval notation. g(x)=log⁡(x2+8)g ( x ) = \log \left( x ^ { 2 } + 8 \right)g(x)=log(x2+8)

Find the domain of the function and express the domain in interval notation. f(x)=log⁡(5x+5)f ( x ) = \log ( 5 x + 5 )f(x)=log(5x+5)

Graph the equation by completing the table and plotting points. Round to two decimal places when necessary. f(x)=ex−2f(x)=e^{x-2}f(x)=ex−2 x y 0 2 3 4

Approximate the function value from the graph. (f+g)(0)(f+g)(0)(f+g)(0)

f(x)=x and g(x)=xf ( x ) = \sqrt { x } \text { and } g ( x ) = \sqrt { x }f(x)=x​ and g(x)=x​ are inverse functions because f(x)⋅g(x)=xf ( x ) \cdot g ( x ) = xf(x)⋅g(x)=x

Evaluate without the use of a calculator. log⁡885\log _ { 8 } \sqrt [ 5 ] { 8 }log8​58​

Use a calculator to approximate the logarithm. Round to 4 decimal places. log⁡(7.04×109)\log \left( 7.04 \times 10 ^ { 9 } \right)log(7.04×109)

Linear Equations and Inequalities in One Variable

Linear Equations in Two Variables and Functions

Systems of Linear Equations and Inequalities

Polynomials

Rational Expressions and Rational Equations

Radicals and Complex Numbers

Quadratic Equations, Functions and Inequalities

Conic Sections

Binomial Expansions, Sequences, and Series

Online: Transformations, Piecewise-Defined Functions, and Probability

Filters

Write an equation of the inverse for the one-to-one function $f ( x ) = 5 x ^ { 3 } - 5$

Graph y = f (x). $f ( x ) = \log _ { 4 } x$

Solve the logarithmic equation. $\log _ { 9 } k + \log _ { 9 } ( 2 k + 9 ) = 2$

Write the expression as a single logarithm. Assume all variables represent positive real numbers. $\log _ { b } x - \log _ { b } x ^ { 6 } + \log _ { b } x ^ { 8 }$

When money is invested at an interest rate of 4%, the value of the investment after t years is given by $A = P ( 1.04 ) ^ { t }$ where P is the original investment. If $24,000 is invested, how long would it take to reach a value of $36,000? Round to the nearest tenth of a year.

Solve the logarithmic equation. $\log ( x + - 2 ) = \log ( 2 x - 6 )$

Solve the logarithmic equation. $6 = 4 - \log _ { 2 } ( 2 x + 4 )$

Solve the logarithmic equation. $\log _ { 9 } ( 5 x + 7 ) - \log _ { 9 } x = \log _ { 9 } 6$

If $f ( x ) = 10 x + 7$ and $g ( x ) = x ^ { 2 } - 7 x$ , find $( f - g ) ( x )$ .

Find the domain of the function and express the domain in interval notation. $g ( x ) = \log \left( x ^ { 2 } + 8 \right)$

Find the domain of the function and express the domain in interval notation. $f ( x ) = \log ( 5 x + 5 )$

Graph the equation by completing the table and plotting points. Round to two decimal places when necessary. $f(x)=e^{x-2}$ x y 0 2 3 4

Approximate the function value from the graph. $(f+g)(0)$

$f ( x ) = \sqrt { x } \text { and } g ( x ) = \sqrt { x }$ are inverse functions because $f ( x ) \cdot g ( x ) = x$

Evaluate without the use of a calculator. $\log _ { 8 } \sqrt [ 5 ] { 8 }$

Use a calculator to approximate the logarithm. Round to 4 decimal places. $\log \left( 7.04 \times 10 ^ { 9 } \right)$