Question 1

Find $( f / g ) ( x )$ .   $f ( x ) = \frac { 1 } { x ^ { 2 } } , g ( x ) = \frac { 1 } { x ^ { 4 } }$

Accepted Answer

A)  $\frac { 1 } { x ^ { 2 } }$ 
B)  $x ^ { 6 }$ 
C)  $\frac { 1 } { x ^ { 4 } }$ 
D)  $\frac { 1 } { x ^ { 6 } }$ 
E)  $x ^ { 2 }$ 
A)  $\frac { 1 } { x ^ { 2 } }$ 
B)  $x ^ { 6 }$ 
C)  $\frac { 1 } { x ^ { 4 } }$ 
D)  $\frac { 1 } { x ^ { 6 } }$ 
E)  $x ^ { 2 }$

Question 2

Which of the following equation does not represent y as a function of x? ​

Accepted Answer

A) y2 = 1 - x 
B) y = x2 + 1 
C) x2 + y = 1 
D) y = x2 + x - 1 
E) y = x2 - 1 
A) y2 = 1 - x 
B) y = x2 + 1 
C) x2 + y = 1 
D) y = x2 + x - 1 
E) y = x2 - 1

Question 3

Find $g \circ g$ . 
 $g ( x ) = x - 2$

Accepted Answer

A)  $( x - 2 ) ^ { 2 }$ 
B)  $x ^ { 2 } - 2$ 
C)  $x + 4$ 
D)  $- x - 4$ 
E)  $x - 4$ 
A)  $( x - 2 ) ^ { 2 }$ 
B)  $x ^ { 2 } - 2$ 
C)  $x + 4$ 
D)  $- x - 4$ 
E)  $x - 4$

Question 4

Select the correct graph of the given function. 
 $f ( x ) = - \frac { 1 } { 6 } x - \frac { 5 } { 2 }$

Accepted Answer

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

Question 5

Which set of ordered pairs represents a function from A to B  
A = {a, b, c} and B = {4, 3, 1, 2}

Accepted Answer

A) {(a, 4), (b, 3)} 
B) {(a, 2), (c, 3), (b,4 )} 
C) {(a, 4), (c, 1)} 
D) {(a, 1), (c, 3), (c, 1), (b, 4)} 
E) {(a, 4), (c, 3), (c, 1), (b, 1)} 
A) {(a, 4), (b, 3)} 
B) {(a, 2), (c, 3), (b,4 )} 
C) {(a, 4), (c, 1)} 
D) {(a, 1), (c, 3), (c, 1), (b, 4)} 
E) {(a, 4), (c, 3), (c, 1), (b, 1)}

Question 6

Use the functions given by $f ( x ) = \frac { 1 } { 8 } x - 5$ and g(x) = x3 to find (g-1 º f-1)(-5).

Accepted Answer

A) -2 
B) 0 
C) -4 
D) 2 
E) 4 
A) -2 
B) 0 
C) -4 
D) 2 
E) 4

Question 7

Determine algebraically whether f and g are inverse functions. $f ( x ) = \sqrt { x + 6 }$ g(x) = x2 - 6, x$\ge$ 0

Accepted Answer

A) True 
 B)False

Question 8

Write the equation of the line that passes through the point P(4, 3) and is perpendicular to the line y = - 5x + 2.

Accepted Answer

A)  $y = \frac { 1 } { 5 } x + 2$ 
B)  $y = \frac { 1 } { 5 } x + 3.8$ 
C)  $y = \frac { 1 } { 5 } x + 2.2$ 
D)  $y = 2.2 x + \frac { 1 } { 5 }$ 
E)  $y = x + 2.2$ 
A)  $y = \frac { 1 } { 5 } x + 2$ 
B)  $y = \frac { 1 } { 5 } x + 3.8$ 
C)  $y = \frac { 1 } { 5 } x + 2.2$ 
D)  $y = 2.2 x + \frac { 1 } { 5 }$ 
E)  $y = x + 2.2$

Question 9

Restrict the domain of the function f so that the function is one-to-one and has an inverse function.Then find the inverse function f-1.State the domains and ranges of f and f-1.

F(x) = (x - 5)2

Accepted Answer

A)  $f ^ { - 1 } ( x ) = \sqrt { x } - 5$ 
The domain of f and the range of f-1 are all real numbers x such that x$\ge$ 5.The domain of f-1 and the range of f are all real numbers x such that x $\ge$ 0. 
B)  $f ^ { - 1 } ( x ) = \sqrt { x } + 5$ 
The domain of f and the range of f-1 are all real numbers x such that x $\ge$ 0.The domain of f-1 and the range of f are all real numbers x such that x $\ge$ -5. 
C)  $f ^ { - 1 } ( x ) = \sqrt { x } + 5$ 
The domain of f and the range of f-1 are all real numbers x such that x $\ge$ 5.The domain of f-1 and the range of f are all real numbers x such that x $\ge$ 0. 
D)  $f ^ { - 1 } ( x ) = \sqrt { x } + 5$ 
The domain of f and the range of f-1 are all real numbers x such that x $\ge$0.The domain of f-1 and the range of f are all real numbers x such that x$\ge$ 5. 
E)  $f ^ { - 1 } ( x ) = \sqrt { x } - 5$ 
The domain of f and the range of f-1 are all real numbers x such that x $\ge$ -5.The domain of f-1 and the range of f are all real numbers x such that x $\ge$ 0. 
A)  $f ^ { - 1 } ( x ) = \sqrt { x } - 5$ 
The domain of f and the range of f-1 are all real numbers x such that x$\ge$ 5.The domain of f-1 and the range of f are all real numbers x such that x $\ge$ 0. 
B)  $f ^ { - 1 } ( x ) = \sqrt { x } + 5$ 
The domain of f and the range of f-1 are all real numbers x such that x $\ge$ 0.The domain of f-1 and the range of f are all real numbers x such that x $\ge$ -5. 
C)  $f ^ { - 1 } ( x ) = \sqrt { x } + 5$ 
The domain of f and the range of f-1 are all real numbers x such that x $\ge$ 5.The domain of f-1 and the range of f are all real numbers x such that x $\ge$ 0. 
D)  $f ^ { - 1 } ( x ) = \sqrt { x } + 5$ 
The domain of f and the range of f-1 are all real numbers x such that x $\ge$0.The domain of f-1 and the range of f are all real numbers x such that x$\ge$ 5. 
E)  $f ^ { - 1 } ( x ) = \sqrt { x } - 5$ 
The domain of f and the range of f-1 are all real numbers x such that x $\ge$ -5.The domain of f-1 and the range of f are all real numbers x such that x $\ge$ 0.

Question 10

Select the correct graph of the given function. 
 $f ( x ) = 1 + \frac { 1 } { x }$

Accepted Answer

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

Question 11

Find the coordinates for the point that is four units to the left of the y-axis and is six units up from the x-axis.

Accepted Answer

A) (-4, -6) 
B) (4, -6) 
C) (-4, 6) 
D) (6, 6) 
E) (4, 6) 
A) (-4, -6) 
B) (4, -6) 
C) (-4, 6) 
D) (6, 6) 
E) (4, 6)

Question 12

Find the inverse of the one-to-one function.

Y = 3x

Accepted Answer

A)  $f ^ { - 1 } ( x ) = 3 x ^ { 2 }$ 
B) f -1(x) = 3x 
C)  $f ^ { - 1 } ( x ) = \frac { x } { 3 }$ 
D)  $f ^ { - 1 } ( x ) = \frac { 3 } { x }$ 
E) f -1(x) = 9x 
A)  $f ^ { - 1 } ( x ) = 3 x ^ { 2 }$ 
B) f -1(x) = 3x 
C)  $f ^ { - 1 } ( x ) = \frac { x } { 3 }$ 
D)  $f ^ { - 1 } ( x ) = \frac { 3 } { x }$ 
E) f -1(x) = 9x

Question 13

Write the equation of the line that passes through the point P (0, 0), and is parallel to the line y = 8x - 1.
​
Write the answer in slope-intercept form.

Accepted Answer

The answer of Write the equation of the line that...

Find $( f / g ) ( x )$ . $f ( x ) = \frac { 1 } { x ^ { 2 } } , g ( x ) = \frac { 1 } { x ^ { 4 } }$

Which of the following equation does not represent y as a function of x?

Find $g \circ g$ . $g ( x ) = x - 2$

Select the correct graph of the given function. $f ( x ) = - \frac { 1 } { 6 } x - \frac { 5 } { 2 }$

Which set of ordered pairs represents a function from A to B A = {a, b, c} and B = {4, 3, 1, 2}

Use the functions given by $f ( x ) = \frac { 1 } { 8 } x - 5$ and g(x) = x³ to find (g^-1 _º f^-1)(-5).

Determine algebraically whether f and g are inverse functions. $f ( x ) = \sqrt { x + 6 }$ g(x) = x² - 6, x $\ge$ 0

Write the equation of the line that passes through the point P(4, 3) and is perpendicular to the line y = - 5x + 2.

Restrict the domain of the function f so that the function is one-to-one and has an inverse function.Then find the inverse function f^-1.State the domains and ranges of f and f^-1. F(x) = (x - 5)²

Select the correct graph of the given function. $f ( x ) = 1 + \frac { 1 } { x }$

Find the coordinates for the point that is four units to the left of the y-axis and is six units up from the x-axis.

Find the inverse of the one-to-one function. Y = 3x

Write the equation of the line that passes through the point P (0, 0), and is parallel to the line y = 8x - 1. Write the answer in slope-intercept form.

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometry

Analytic Trigonometry

Additional Topics In Trigonometery

Systems Of Equations and Inequalities

Matrices and Determinants

Sequences Series and Probability

Topics In Analytic Geometry

Analytic Geometry In Three Dimensions

Limits and An Introduction To Calculus

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Exam 1: Functions and Their Graphs

Find (f/g)(x)( f / g ) ( x )(f/g)(x) . f(x)=1x2,g(x)=1x4f ( x ) = \frac { 1 } { x ^ { 2 } } , g ( x ) = \frac { 1 } { x ^ { 4 } }f(x)=x21​,g(x)=x41​

Which of the following equation does not represent y as a function of x? ​

Find g∘gg \circ gg∘g . g(x)=x−2g ( x ) = x - 2g(x)=x−2

Select the correct graph of the given function. f(x)=−16x−52f ( x ) = - \frac { 1 } { 6 } x - \frac { 5 } { 2 }f(x)=−61​x−25​

Which set of ordered pairs represents a function from A to B A = {a, b, c} and B = {4, 3, 1, 2}

Use the functions given by f(x)=18x−5f ( x ) = \frac { 1 } { 8 } x - 5f(x)=81​x−5 and g(x) = x3 to find (g-1 º f-1)(-5).

Determine algebraically whether f and g are inverse functions. f(x)=x+6f ( x ) = \sqrt { x + 6 }f(x)=x+6​ g(x) = x2 - 6, x ≥\ge≥ 0

Write the equation of the line that passes through the point P(4, 3) and is perpendicular to the line y = - 5x + 2.

Restrict the domain of the function f so that the function is one-to-one and has an inverse function.Then find the inverse function f-1.State the domains and ranges of f and f-1. F(x) = (x - 5)2

Select the correct graph of the given function. f(x)=1+1xf ( x ) = 1 + \frac { 1 } { x }f(x)=1+x1​

Find the coordinates for the point that is four units to the left of the y-axis and is six units up from the x-axis.

Find the inverse of the one-to-one function. Y = 3x

Write the equation of the line that passes through the point P (0, 0), and is parallel to the line y = 8x - 1. ​ Write the answer in slope-intercept form.

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometry

Analytic Trigonometry

Additional Topics In Trigonometery

Systems Of Equations and Inequalities

Matrices and Determinants

Sequences Series and Probability

Topics In Analytic Geometry

Analytic Geometry In Three Dimensions

Limits and An Introduction To Calculus

Filters

Find $( f / g ) ( x )$ . $f ( x ) = \frac { 1 } { x ^ { 2 } } , g ( x ) = \frac { 1 } { x ^ { 4 } }$

Which of the following equation does not represent y as a function of x?

Find $g \circ g$ . $g ( x ) = x - 2$

Select the correct graph of the given function. $f ( x ) = - \frac { 1 } { 6 } x - \frac { 5 } { 2 }$

Use the functions given by $f ( x ) = \frac { 1 } { 8 } x - 5$ and g(x) = x³ to find (g^-1 _º f^-1)(-5).

Determine algebraically whether f and g are inverse functions. $f ( x ) = \sqrt { x + 6 }$ g(x) = x² - 6, x $\ge$ 0

Restrict the domain of the function f so that the function is one-to-one and has an inverse function.Then find the inverse function f^-1.State the domains and ranges of f and f^-1. F(x) = (x - 5)²

Select the correct graph of the given function. $f ( x ) = 1 + \frac { 1 } { x }$

Write the equation of the line that passes through the point P (0, 0), and is parallel to the line y = 8x - 1. Write the answer in slope-intercept form.