Find the inverse function of g(x) = x2 - 3 informally.

A) $g ^ { - 1 } ( x ) = \sqrt [ 2 ] { x - 3 }$ B) $g ^ { - 1 } ( x ) = ( x + 3 ) ^ { 2 }$ C) $g ^ { - 1 } ( x ) = x ^ { 2 } + 3$ D) $g ^ { - 1 } ( x ) = \sqrt [ 2 ] { x + 3 }$ E) $g ^ { - 1 } ( x ) = ( x - 3 ) ^ { 2 }$ A) $g ^ { - 1 } ( x ) = \sqrt [ 2 ] { x - 3 }$ B) $g ^ { - 1 } ( x ) = ( x + 3 ) ^ { 2 }$ C) $g ^ { - 1 } ( x ) = x ^ { 2 } + 3$ D) $g ^ { - 1 } ( x ) = \sqrt [ 2 ] { x + 3 }$ E) $g ^ { - 1 } ( x ) = ( x - 3 ) ^ { 2 }$

Exam 1: Functions and Their Graphs

Find the center and radius of the circle, and sketch its graph. $\left( x - \frac { 1 } { 2 } \right) ^ { 2 } + \left( y - \frac { 1 } { 2 } \right) ^ { 2 } = \frac { 49 } { 4 }$

(Multiple Choice)

4.9/5

(31)

Question 261

Select the correct graph, showing f and g are inverse functions. $f ( x ) = 6 x + 1 , g ( x ) = \frac { x - 1 } { 6 }$

(Multiple Choice)

5.0/5

(33)

Question 262

A discount outlet is offering a 70% discount on all items.Select a linear equation giving the sale price S for an item with a list price L.

(Multiple Choice)

4.9/5

(34)

Question 263

Find a mathematical model representing the statement.(Determine the constant of proportionality.) Y varies inversely as x. $( y = 9 \text { when } x = 45 . )$

(Multiple Choice)

4.9/5

(29)

Question 264

Identify the parent function and the transformation shown in the graph.Write an equation for the function shown in the graph.

(Multiple Choice)

4.7/5

(38)

Question 265

Identify the parent function and the transformation shown in the graph.Write an equation for the function shown in the graph.

(Multiple Choice)

4.9/5

(35)

Question 266

Find ( fg )(x). $f ( x ) = \sqrt { 3 x } \quad g ( x ) = \sqrt { 5 x + 7 }$

(Multiple Choice)

4.8/5

(38)

Question 267

Evaluate the indicated function for $f ( x ) = x ^ { 2 } + 6$ and $g ( x ) = x - 5$ . $( f / g ) ( - 4 ) - g ( 6 )$

(Multiple Choice)

5.0/5

(34)

Question 268

Find $f \circ g$ and the domain of the composite function. $f ( x ) = | x | , g ( x ) = x + 3$

(Multiple Choice)

4.9/5

(38)

Question 269

Approximate the coordinates of the points.

(Multiple Choice)

4.8/5

(26)

Question 270

Find the slope-intercept form of the equation of the line passing through the points.Select the correct answer for the line. $P ( 6 , - 2 ) , Q ( - 6,6 )$

(Multiple Choice)

4.9/5

(44)

Question 271

Write the standard form of the equation of the circle with the given characteristics. center: (-1, -5); radius: 6

(Multiple Choice)

4.8/5

(19)

Question 272

Let M denote the midpoint of the line segment joining (4, 3) and (11, 6).Find the distance from M to the point (-6, -5).Round the answer to the nearest tenth.

(Multiple Choice)

4.9/5

(37)

Question 273

Does the function have an inverse function?

(True/False)

4.8/5

(33)

Question 274

Find the distance between the points. (-9, 4), (3, -5)

(Multiple Choice)

4.9/5

(41)

Question 275

The number of people playing tennis T (in millions) in the United States from 2000 through 2007 can be approximated by the function $T ( t ) = 0.0235 t ^ { 4 } - 0.3401 t ^ { 3 } + 2.556 t ^ { 2 } - 6.86 t + 23.8$ And the U.S.population P (in millions) from 2000 through 2007 can be approximated by the function $P ( t ) = 5.8 t + 224.5$ , where t represents the year, with t = 0 corresponding to 2000. Evaluate the function $h ( t ) = \frac { 0.0235 t ^ { 4 } - 0.3401 t ^ { 3 } + 2.556 t ^ { 2 } - 6.86 t + 23.8 } { 5.8 t + 224.5 }$ for t = 0 and 3.

(Multiple Choice)

4.8/5

(32)

Question 276

Given the points (-6, -8) and (4, -6).Find a third point so that the three points form the vertices of a right triangle.

(Multiple Choice)

4.9/5

(40)

Question 277

Find the x- and y-intercepts of the graph of the equation $y ^ { 2 } = 8 x + 5$ .

(Multiple Choice)

4.8/5

(34)

Question 278

Find the inverse function of g(x) = x² - 3 informally.

(Multiple Choice)

4.8/5

(29)

Question 279

The monthly cost C of running the machinery in a factory for t hours is given by $C ( t ) = 40 t + 400$ The number of hours t needed to produce x products is given by $t ( x ) = 6 x$ . Find the equation representing the cost C of manufacturing x products.

(Multiple Choice)

4.9/5

(32)

Question 280

Find the center and radius of the circle, and sketch its graph. $\left( x - \frac { 1 } { 2 } \right) ^ { 2 } + \left( y - \frac { 1 } { 2 } \right) ^ { 2 } = \frac { 49 } { 4 }$

Select the correct graph, showing f and g are inverse functions. $f ( x ) = 6 x + 1 , g ( x ) = \frac { x - 1 } { 6 }$

A discount outlet is offering a 70% discount on all items.Select a linear equation giving the sale price S for an item with a list price L.

Find a mathematical model representing the statement.(Determine the constant of proportionality.) Y varies inversely as x. $( y = 9 \text { when } x = 45 . )$

Identify the parent function and the transformation shown in the graph.Write an equation for the function shown in the graph.

Identify the parent function and the transformation shown in the graph.Write an equation for the function shown in the graph.

Find ( fg )(x). $f ( x ) = \sqrt { 3 x } \quad g ( x ) = \sqrt { 5 x + 7 }$

Evaluate the indicated function for $f ( x ) = x ^ { 2 } + 6$ and $g ( x ) = x - 5$ . $( f / g ) ( - 4 ) - g ( 6 )$

Find $f \circ g$ and the domain of the composite function. $f ( x ) = | x | , g ( x ) = x + 3$

Approximate the coordinates of the points.

Find the slope-intercept form of the equation of the line passing through the points.Select the correct answer for the line. $P ( 6 , - 2 ) , Q ( - 6,6 )$

Write the standard form of the equation of the circle with the given characteristics. center: (-1, -5); radius: 6

Let M denote the midpoint of the line segment joining (4, 3) and (11, 6).Find the distance from M to the point (-6, -5).Round the answer to the nearest tenth.

Does the function have an inverse function?

Find the distance between the points. (-9, 4), (3, -5)

Given the points (-6, -8) and (4, -6).Find a third point so that the three points form the vertices of a right triangle.

Find the x- and y-intercepts of the graph of the equation $y ^ { 2 } = 8 x + 5$ .

Find the inverse function of g(x) = x² - 3 informally.

The monthly cost C of running the machinery in a factory for t hours is given by $C ( t ) = 40 t + 400$ The number of hours t needed to produce x products is given by $t ( x ) = 6 x$ . Find the equation representing the cost C of manufacturing x products.

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

Exam 1: Functions and Their Graphs

Find the center and radius of the circle, and sketch its graph. (x−12)2+(y−12)2=494\left( x - \frac { 1 } { 2 } \right) ^ { 2 } + \left( y - \frac { 1 } { 2 } \right) ^ { 2 } = \frac { 49 } { 4 }(x−21​)2+(y−21​)2=449​

Select the correct graph, showing f and g are inverse functions. f(x)=6x+1,g(x)=x−16f ( x ) = 6 x + 1 , g ( x ) = \frac { x - 1 } { 6 }f(x)=6x+1,g(x)=6x−1​

A discount outlet is offering a 70% discount on all items.Select a linear equation giving the sale price S for an item with a list price L.

Find a mathematical model representing the statement.(Determine the constant of proportionality.) Y varies inversely as x. (y=9 when x=45.)( y = 9 \text { when } x = 45 . )(y=9 when x=45.)

Identify the parent function and the transformation shown in the graph.Write an equation for the function shown in the graph.

Identify the parent function and the transformation shown in the graph.Write an equation for the function shown in the graph.

Find ( fg )(x). f(x)=3xg(x)=5x+7f ( x ) = \sqrt { 3 x } \quad g ( x ) = \sqrt { 5 x + 7 }f(x)=3x​g(x)=5x+7​

Evaluate the indicated function for f(x)=x2+6f ( x ) = x ^ { 2 } + 6f(x)=x2+6 and g(x)=x−5g ( x ) = x - 5g(x)=x−5 . (f/g)(−4)−g(6)( f / g ) ( - 4 ) - g ( 6 )(f/g)(−4)−g(6)

Find f∘gf \circ gf∘g and the domain of the composite function. f(x)=∣x∣,g(x)=x+3f ( x ) = | x | , g ( x ) = x + 3f(x)=∣x∣,g(x)=x+3

Approximate the coordinates of the points.

Find the slope-intercept form of the equation of the line passing through the points.Select the correct answer for the line. P(6,−2),Q(−6,6)P ( 6 , - 2 ) , Q ( - 6,6 )P(6,−2),Q(−6,6)

Write the standard form of the equation of the circle with the given characteristics. center: (-1, -5); radius: 6

Let M denote the midpoint of the line segment joining (4, 3) and (11, 6).Find the distance from M to the point (-6, -5).Round the answer to the nearest tenth. ​

Does the function have an inverse function?

Find the distance between the points. ​ (-9, 4), (3, -5) ​

Given the points (-6, -8) and (4, -6).Find a third point so that the three points form the vertices of a right triangle. ​

Find the x- and y-intercepts of the graph of the equation y2=8x+5y ^ { 2 } = 8 x + 5y2=8x+5 .

Find the inverse function of g(x) = x2 - 3 informally.

The monthly cost C of running the machinery in a factory for t hours is given by C(t)=40t+400C ( t ) = 40 t + 400C(t)=40t+400 The number of hours t needed to produce x products is given by t(x)=6xt ( x ) = 6 xt(x)=6x . Find the equation representing the cost C of manufacturing x products.

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 the center and radius of the circle, and sketch its graph. $\left( x - \frac { 1 } { 2 } \right) ^ { 2 } + \left( y - \frac { 1 } { 2 } \right) ^ { 2 } = \frac { 49 } { 4 }$

Select the correct graph, showing f and g are inverse functions. $f ( x ) = 6 x + 1 , g ( x ) = \frac { x - 1 } { 6 }$

Find a mathematical model representing the statement.(Determine the constant of proportionality.) Y varies inversely as x. $( y = 9 \text { when } x = 45 . )$

Find ( fg )(x). $f ( x ) = \sqrt { 3 x } \quad g ( x ) = \sqrt { 5 x + 7 }$

Evaluate the indicated function for $f ( x ) = x ^ { 2 } + 6$ and $g ( x ) = x - 5$ . $( f / g ) ( - 4 ) - g ( 6 )$

Find $f \circ g$ and the domain of the composite function. $f ( x ) = | x | , g ( x ) = x + 3$

Find the slope-intercept form of the equation of the line passing through the points.Select the correct answer for the line. $P ( 6 , - 2 ) , Q ( - 6,6 )$

Let M denote the midpoint of the line segment joining (4, 3) and (11, 6).Find the distance from M to the point (-6, -5).Round the answer to the nearest tenth.

Find the distance between the points. (-9, 4), (3, -5)

Given the points (-6, -8) and (4, -6).Find a third point so that the three points form the vertices of a right triangle.

Find the x- and y-intercepts of the graph of the equation $y ^ { 2 } = 8 x + 5$ .

Find the inverse function of g(x) = x² - 3 informally.

The monthly cost C of running the machinery in a factory for t hours is given by $C ( t ) = 40 t + 400$ The number of hours t needed to produce x products is given by $t ( x ) = 6 x$ . Find the equation representing the cost C of manufacturing x products.