Question 1

If $f ( x ) = x ^ { 3 } - 5$ and $g ( x ) = \sqrt [ 3 ] { x + 5 }$, then which of the following is/are true?

Accepted Answer

A)  $( f \circ g ) ( x ) = x$ and $( g \circ f ) ( x ) = x$ 
B)  $f$ is the inverse function of $g$ 
C)  $g$ is the inverse function of $f$ 
D)  All of the above are true. 
A)  $( f \circ g ) ( x ) = x$ and $( g \circ f ) ( x ) = x$ 
B)  $f$ is the inverse function of $g$ 
C)  $g$ is the inverse function of $f$ 
D)  All of the above are true.

Question 2

Scientists often use a process called carbon dating to estimate the age of archaeological finds. The process measures the amount of carbon-14, a radioactive isotope with a half-life of 5730 years. If a sample of wood from an ancient artifact had 13 grams of carbon-14 initially, the amount remaining, in grams, is given by $A ( t ) = 13 \left( \frac { 1 } { 2 } \right) ^ { t / 5730 }$ where t is the number of years since the tree died. How many grams would be present after 22,920 years?

Accepted Answer

The answer of Scientists often use a process called carbon...

Question 3

Evaluate without the use of a calculator. $\log _ { 6 } \frac { 1 } { 36 }$

Accepted Answer

A)  -2 
B)  4 
C)  12 
D)  2 
A)  -2 
B)  4 
C)  12 
D)  2

Question 4

Solve the logarithmic equation. $$\log _ { 3 } x = 7$$

Accepted Answer

A)  $\left\{ 7 ^ { 3 } \right\}$ 
B)  $\left\{ 3 ^ { 7 } \right\}$ 
C)  $\{ 0.5646 \}$ 
D)  $\{ 1.7712 \}$ 
A)  $\left\{ 7 ^ { 3 } \right\}$ 
B)  $\left\{ 3 ^ { 7 } \right\}$ 
C)  $\{ 0.5646 \}$ 
D)  $\{ 1.7712 \}$

If $f ( x ) = x ^ { 3 } - 5$ and $g ( x ) = \sqrt [ 3 ] { x + 5 }$ , then which of the following is/are true?

Evaluate without the use of a calculator. $\log _ { 6 } \frac { 1 } { 36 }$

Solve the logarithmic equation. $\log _ { 3 } x = 7$

Linear Equations and Inequalities in One Variable

Linear Equations in Two Variables and Functions

Systems of Linear Equations and Inequalities

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Rational Expressions and Rational Equations

Radicals and Complex Numbers

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Conic Sections

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Online: Transformations, Piecewise-Defined Functions, and Probability

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Exam 8: Exponential and Logarithmic Functions and Applications

If f(x)=x3−5f ( x ) = x ^ { 3 } - 5f(x)=x3−5 and g(x)=x+53g ( x ) = \sqrt [ 3 ] { x + 5 }g(x)=3x+5​ , then which of the following is/are true?

Evaluate without the use of a calculator. log⁡6136\log _ { 6 } \frac { 1 } { 36 }log6​361​

Solve the logarithmic equation. log⁡3x=7\log _ { 3 } x = 7log3​x=7

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

If $f ( x ) = x ^ { 3 } - 5$ and $g ( x ) = \sqrt [ 3 ] { x + 5 }$ , then which of the following is/are true?

Evaluate without the use of a calculator. $\log _ { 6 } \frac { 1 } { 36 }$

Solve the logarithmic equation. $\log _ { 3 } x = 7$