Find f132 if f1x2 = -4x2 + 5x. (pp. 6263)
Read moreTable of Contents
A.1
Algebra Essentials
A.10
nth Roots; Rational Exponents
A.2
Geometry Essentials
A.3
Polynomials
A.4
Synthetic Division
A.5
Rational Expressions
A.6
Solving Equations
A.7
Complex Numbers; Quadratic Equations in the Complex Number System
A.8
Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate Job Applications
A.9
Interval Notation; Solving Inequalities
Appendix B
The Limit of a Sequence; Infinite Series
1
Graphs
1.1
The Distance and Midpoint Formulas; Graphing Utilities; Introduction to Graphing Equations
1.2
Intercepts; Symmetry; Graphing Key Equations
1.3
Solving Equations Using a Graphing Utility
1.4
Lines
1.5
Circles
2
Functions and Their Graphs
2.1
Functions
2.2
The Graph of a Function
2.3
Properties of Functions
2.4
Library of Functions; Piecewise-defined Functions
2.5
Graphing Techniques: Transformations
2.6
Mathematical Models: Building Functions
3
Linear and Quadratic Functions
3.1
Linear Functions and Their Properties
3.2
Linear Models: Building Linear Functions from Data
3.3
Quadratic Functions and Their Properties
3.4
Build Quadratic Models from Verbal Descriptions and from Data
3.5
Inequalities Involving Quadratic Functions
4
Polynomial and Rational Functions
4.1
Polynomial Functions and Models
4.2
The Real Zeros of a Polynomial Function
4.3
Complex Zeros; Fundamental Theorem of Algebra
4.4
Properties of Rational Functions
4.5
The Graph of a Rational Function
4.6
Polynomial and Rational Inequalities
4.7
Polynomial and Rational Functions
5
Exponential and Logarithmic Functions
5.1
Composite Functions
5.2
One-to-One Functions; Inverse Functions
5.3
Exponential Functions
5.4
Logarithmic Functions
5.5
Properties of Logarithms
5.6
Logarithmic and Exponential Equations
5.7
Financial Models
5.70
Financial Models
5.8
Exponential Growth and Decay Models; Newtons Law; Logistic Growth and Decay Models
5.80
Exponential Growth and Decay Models; Newtons Law; Logistic Growth and Decay Models
5.9
Building Exponential, Logarithmic, and Logistic Models from Data
6
Trigonometric Functions
6.1
Angles and Their Measure
6.2
Trigonometric Functions: Unit Circle Approach
6.3
Properties of the Trigonometric Functions
6.4
Graphs of the Sine and Cosine Functions
6.5
Open the Period applet. On the screen you will see a slider. Move the point along the slider to see the role v plays in the graph of f1x2 = sin1vx2. Pay particular attention to the key points matched by color on each graph. For convenience the graph of g1
6.6
Phase Shift; Sinusoidal Curve Fitting 4
7
Analytic Trigonometry
7.1
The Inverse Sine, Cosine, and Tangent Functions
7.2
The Inverse Trigonometric Functions (Continued)
7.3
Trigonometric Equations
7.4
Trigonometric Identities
7.5
Sum and Difference Formulas
7.6
Double-angle and Half-angle Formulas
7.7
Product-to-Sum and Sum-to-Product Formulas
8
Applications of Trigonometric Functions
8.1
Right Triangle Trigonometry; Applications
8.2
The Law of Sines
8.3
The Law of Cosines
8.4
Area of a Triangle
8.5
Simple Harmonic Motion; Damped Motion; Combining Waves
9
Polar Coordinates; Vectors
9.1
Polar Coordinates
9.2
Polar Equations and Graphs
9.3
The Complex Plane; De Moivres Theorem
9.4
Vectors
9.5
The Dot Product
9.6
Vectors in Space
9.7
The Cross Product
10
Analytic Geometry
10.1
Conics
10.2
The Parabola
10.3
The Ellipse
10.4
The Hyperbola
10.5
Rotation of Axes; General Form of a Conic
10.6
Polar Equations of Conics
10.7
Plane Curves and Parametric Equations
11
Systems of Equations and Inequalities
11.1
Systems of Linear Equations: Substitution and Elimination
11.2
Systems of Linear Equations: Matrices
11.3
Systems of Linear Equations: Determinants
11.4
Matrix Algebra
11.5
Partial Fraction Decomposition
11.6
Systems of Nonlinear Equations
11.7
Systems of Inequalities
11.8
Linear Programming
12
Sequences; Induction; the Binomial Theorem
12.1
Sequences
12.2
Arithmetic Sequences
12.3
Geometric Sequences; Geometric Series
12.4
Mathematical Induction
12.5
The Binomial Theorem
13
Sequences; Induction; the Binomial Theorem
13.1
Sequences; Induction; the Binomial Theorem
13.2
Probability
14
Sequences; Induction; the Binomial Theorem
14.1
Finding Limits Using Tables and Graphs
14.2
Algebra Techniques for Finding Limits
14.3
One-sided Limits; Continuous Functions
14.4
The Tangent Problem; The Derivative
14.5
The Area Problem; The Integral
15
Sequences; Induction; the Binomial Theorem
16
Sequences; Induction; the Binomial Theorem
17
Sequences; Induction; the Binomial Theorem
Textbook Solutions for Precalculus Enhanced with Graphing Utilities
Chapter 5.1 Problem 70
Question
The price p, in dollars, of a certain commodity and the quantity x sold obey the demand equation p = - 1 5 x + 200 0 x 1000 Suppose that the cost C, in dollars, of producing x units is C = 1x 10 + 400 Assuming that all items produced are sold, find the cost C as a function of the price p
Solution
The first step in solving 5.1 problem number 70 trying to solve the problem we have to refer to the textbook question: The price p, in dollars, of a certain commodity and the quantity x sold obey the demand equation p = - 1 5 x + 200 0 x 1000 Suppose that the cost C, in dollars, of producing x units is C = 1x 10 + 400 Assuming that all items produced are sold, find the cost C as a function of the price p
From the textbook chapter Composite Functions you will find a few key concepts needed to solve this.
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Title
Precalculus Enhanced with Graphing Utilities 6
Author
Michael Sullivan
ISBN
9780132854351
The price p, in dollars, of a certain commodity and the
Chapter 5.1 textbook questions
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Chapter 5: Problem 1 Precalculus Enhanced with Graphing Utilities 6
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Chapter 5: Problem 2 Precalculus Enhanced with Graphing Utilities 6
Findf13x2 if f1x2 = 4 - 2x2 . (pp. 6263)
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Chapter 5: Problem 3 Precalculus Enhanced with Graphing Utilities 6
Find the domain of the function f1x2 = x2 - 1 x2 - 25 . (pp. 6465)
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Chapter 5: Problem 4 Precalculus Enhanced with Graphing Utilities 6
Given two functions f and g, the , denoted f g, is defined by 1f g2 1x2 = .
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Chapter 5: Problem 5 Precalculus Enhanced with Graphing Utilities 6
f1g1x22 = f1x2 # g1x2.
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Chapter 5: Problem 6 Precalculus Enhanced with Graphing Utilities 6
The domain of the composite function 1f g2 1x2 is the same as the domain of g1x2.
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Chapter 5: Problem 7 Precalculus Enhanced with Graphing Utilities 6
In Problems 7 and 8, evaluate each expression using the values given in the table.
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Chapter 5: Problem 8 Precalculus Enhanced with Graphing Utilities 6
In Problems 7 and 8, evaluate each expression using the values given in the table.
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Chapter 5: Problem 9 Precalculus Enhanced with Graphing Utilities 6
In Problems 9 and 10, evaluate each expression using the graphs of y = f1x2 and y = g1x2 shown in the figure.
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Chapter 5: Problem 10 Precalculus Enhanced with Graphing Utilities 6
In Problems 9 and 10, evaluate each expression using the graphs of y = f1x2 and y = g1x2 shown in the figure.
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Chapter 5: Problem 11 Precalculus Enhanced with Graphing Utilities 6
In Problems 1120, for the given functions f and g, find: (a) 1f g2142 (b) 1g f 2122 (c) 1f f 2112 (d) (g g)102
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Chapter 5: Problem 12 Precalculus Enhanced with Graphing Utilities 6
In Problems 1120, for the given functions f and g, find: (a) 1f g2142 (b) 1g f 2122 (c) 1f f 2112 (d) (g g)103
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Chapter 5: Problem 13 Precalculus Enhanced with Graphing Utilities 6
In Problems 1120, for the given functions f and g, find: (a) 1f g2142 (b) 1g f 2122 (c) 1f f 2112 (d) (g g)104
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Chapter 5: Problem 14 Precalculus Enhanced with Graphing Utilities 6
In Problems 1120, for the given functions f and g, find: (a) 1f g2142 (b) 1g f 2122 (c) 1f f 2112 (d) (g g)105
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Chapter 5: Problem 15 Precalculus Enhanced with Graphing Utilities 6
In Problems 1120, for the given functions f and g, find: (a) 1f g2142 (b) 1g f 2122 (c) 1f f 2112 (d) (g g)106
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Chapter 5: Problem 16 Precalculus Enhanced with Graphing Utilities 6
In Problems 1120, for the given functions f and g, find: (a) 1f g2142 (b) 1g f 2122 (c) 1f f 2112 (d) (g g)107
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Chapter 5: Problem 17 Precalculus Enhanced with Graphing Utilities 6
In Problems 1120, for the given functions f and g, find: (a) 1f g2142 (b) 1g f 2122 (c) 1f f 2112 (d) (g g)108
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Chapter 5: Problem 18 Precalculus Enhanced with Graphing Utilities 6
In Problems 1120, for the given functions f and g, find: (a) 1f g2142 (b) 1g f 2122 (c) 1f f 2112 (d) (g g)109
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Chapter 5: Problem 19 Precalculus Enhanced with Graphing Utilities 6
In Problems 1120, for the given functions f and g, find: (a) 1f g2142 (b) 1g f 2122 (c) 1f f 2112 (d) (g g)110
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Chapter 5: Problem 20 Precalculus Enhanced with Graphing Utilities 6
In Problems 1120, for the given functions f and g, find: (a) 1f g2142 (b) 1g f 2122 (c) 1f f 2112 (d) (g g)111
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Chapter 5: Problem 21 Precalculus Enhanced with Graphing Utilities 6
In Problems 2128, find the domain of the composite function f g.
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Chapter 5: Problem 22 Precalculus Enhanced with Graphing Utilities 6
In Problems 2128, find the domain of the composite function f g.
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Chapter 5: Problem 23 Precalculus Enhanced with Graphing Utilities 6
In Problems 2128, find the domain of the composite function f g.
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Chapter 5: Problem 24 Precalculus Enhanced with Graphing Utilities 6
In Problems 2128, find the domain of the composite function f g.
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Chapter 5: Problem 25 Precalculus Enhanced with Graphing Utilities 6
In Problems 2128, find the domain of the composite function f g.
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Chapter 5: Problem 26 Precalculus Enhanced with Graphing Utilities 6
In Problems 2128, find the domain of the composite function f g.
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Chapter 5: Problem 27 Precalculus Enhanced with Graphing Utilities 6
In Problems 2128, find the domain of the composite function f g.
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Chapter 5: Problem 28 Precalculus Enhanced with Graphing Utilities 6
In Problems 2128, find the domain of the composite function f g.
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Chapter 5: Problem 29 Precalculus Enhanced with Graphing Utilities 6
In Problems 29 44, for the given functions f and g, find: (a) f g (b) g f (c) f f (d) g g State the domain of each composite function.
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Chapter 5: Problem 30 Precalculus Enhanced with Graphing Utilities 6
In Problems 29 44, for the given functions f and g, find: (a) f g (b) g f (c) f f (d) g g State the domain of each composite function.
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Chapter 5: Problem 31 Precalculus Enhanced with Graphing Utilities 6
In Problems 29 44, for the given functions f and g, find: (a) f g (b) g f (c) f f (d) g g State the domain of each composite function.
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Chapter 5: Problem 32 Precalculus Enhanced with Graphing Utilities 6
In Problems 29 44, for the given functions f and g, find: (a) f g (b) g f (c) f f (d) g g State the domain of each composite function.
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Chapter 5: Problem 33 Precalculus Enhanced with Graphing Utilities 6
In Problems 29 44, for the given functions f and g, find: (a) f g (b) g f (c) f f (d) g g State the domain of each composite function.
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Chapter 5: Problem 34 Precalculus Enhanced with Graphing Utilities 6
In Problems 29 44, for the given functions f and g, find: (a) f g (b) g f (c) f f (d) g g State the domain of each composite function.
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Chapter 5: Problem 35 Precalculus Enhanced with Graphing Utilities 6
In Problems 29 44, for the given functions f and g, find: (a) f g (b) g f (c) f f (d) g g State the domain of each composite function.
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Chapter 5: Problem 36 Precalculus Enhanced with Graphing Utilities 6
In Problems 29 44, for the given functions f and g, find: (a) f g (b) g f (c) f f (d) g g State the domain of each composite function.
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Chapter 5: Problem 37 Precalculus Enhanced with Graphing Utilities 6
In Problems 29 44, for the given functions f and g, find: (a) f g (b) g f (c) f f (d) g g State the domain of each composite function.
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Chapter 5: Problem 38 Precalculus Enhanced with Graphing Utilities 6
In Problems 29 44, for the given functions f and g, find: (a) f g (b) g f (c) f f (d) g g State the domain of each composite function.
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Chapter 5: Problem 39 Precalculus Enhanced with Graphing Utilities 6
In Problems 29 44, for the given functions f and g, find: (a) f g (b) g f (c) f f (d) g g State the domain of each composite function.
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Chapter 5: Problem 40 Precalculus Enhanced with Graphing Utilities 6
In Problems 29 44, for the given functions f and g, find: (a) f g (b) g f (c) f f (d) g g State the domain of each composite function.
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Chapter 5: Problem 41 Precalculus Enhanced with Graphing Utilities 6
In Problems 29 44, for the given functions f and g, find: (a) f g (b) g f (c) f f (d) g g State the domain of each composite function.
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Chapter 5: Problem 42 Precalculus Enhanced with Graphing Utilities 6
In Problems 29 44, for the given functions f and g, find: (a) f g (b) g f (c) f f (d) g g State the domain of each composite function.
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Chapter 5: Problem 43 Precalculus Enhanced with Graphing Utilities 6
In Problems 29 44, for the given functions f and g, find: (a) f g (b) g f (c) f f (d) g g State the domain of each composite function.
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Chapter 5: Problem 44 Precalculus Enhanced with Graphing Utilities 6
In Problems 29 44, for the given functions f and g, find: (a) f g (b) g f (c) f f (d) g g State the domain of each composite function.
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Chapter 5: Problem 45 Precalculus Enhanced with Graphing Utilities 6
In Problems 4552, show that 1f g2 1x2 = 1g f2 1x2 = x.
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Chapter 5: Problem 46 Precalculus Enhanced with Graphing Utilities 6
In Problems 4552, show that 1f g2 1x2 = 1g f2 1x2 = x.
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Chapter 5: Problem 47 Precalculus Enhanced with Graphing Utilities 6
In Problems 4552, show that 1f g2 1x2 = 1g f2 1x2 = x.
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Chapter 5: Problem 48 Precalculus Enhanced with Graphing Utilities 6
In Problems 4552, show that 1f g2 1x2 = 1g f2 1x2 = x.
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Chapter 5: Problem 49 Precalculus Enhanced with Graphing Utilities 6
In Problems 4552, show that 1f g2 1x2 = 1g f2 1x2 = x.
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Chapter 5: Problem 50 Precalculus Enhanced with Graphing Utilities 6
In Problems 4552, show that 1f g2 1x2 = 1g f2 1x2 = x.
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Chapter 5: Problem 51 Precalculus Enhanced with Graphing Utilities 6
In Problems 4552, show that 1f g2 1x2 = 1g f2 1x2 = x.
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Chapter 5: Problem 52 Precalculus Enhanced with Graphing Utilities 6
In Problems 4552, show that 1f g2 1x2 = 1g f2 1x2 = x.
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Chapter 5: Problem 53 Precalculus Enhanced with Graphing Utilities 6
In Problems 5358, find functions f and g so that f g = H.
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Chapter 5: Problem 54 Precalculus Enhanced with Graphing Utilities 6
In Problems 5358, find functions f and g so that f g = H.
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Chapter 5: Problem 55 Precalculus Enhanced with Graphing Utilities 6
In Problems 5358, find functions f and g so that f g = H.
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Chapter 5: Problem 56 Precalculus Enhanced with Graphing Utilities 6
In Problems 5358, find functions f and g so that f g = H.
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Chapter 5: Problem 57 Precalculus Enhanced with Graphing Utilities 6
In Problems 5358, find functions f and g so that f g = H.
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Chapter 5: Problem 58 Precalculus Enhanced with Graphing Utilities 6
In Problems 5358, find functions f and g so that f g = H.
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Chapter 5: Problem 59 Precalculus Enhanced with Graphing Utilities 6
If f1x2 = 2x3 - 3x2 + 4x - 1 and g1x2 = 2, find 1f g2 1x2 and 1g f2 1x2.
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Chapter 5: Problem 60 Precalculus Enhanced with Graphing Utilities 6
If f1x2 = x + 1 x - 1 , find 1f f2 1x2.
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Chapter 5: Problem 61 Precalculus Enhanced with Graphing Utilities 6
If f1x2 = 2x2 + 5 and g1x2 = 3x + a, find a so that the graph of f g crosses the y-axis at 23.
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Chapter 5: Problem 62 Precalculus Enhanced with Graphing Utilities 6
If f1x2 = 3x2 - 7 and g1x2 = 2x + a, find a so that the graph of f g crosses the y-axis at 68.
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Chapter 5: Problem 63 Precalculus Enhanced with Graphing Utilities 6
In Problems 63 and 64, use the functions f and g to find: (a) f g (b) g f (c) the domain of f g and of g f (d) the conditions for which f g = g f
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Chapter 5: Problem 64 Precalculus Enhanced with Graphing Utilities 6
In Problems 63 and 64, use the functions f and g to find: (a) f g (b) g f (c) the domain of f g and of g f (d) the conditions for which f g = g f
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Chapter 5: Problem 65 Precalculus Enhanced with Graphing Utilities 6
The surface area S (in square meters) of a hot-air balloon is given by S(r) = 4pr2 where r is the radius of the balloon (in meters). If the radius r is increasing with time t (in seconds) according to the formula r1t2 = 2 3 t 3 , t 0, find the surface area S of the balloon as a function of the time t.
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Chapter 5: Problem 66 Precalculus Enhanced with Graphing Utilities 6
he volume V (in cubic meters) of the hot-air balloon described in Problem 65 is given by V(r) = 4 3 pr3 . If the radius r is the same function of t as in Problem 65, find the volume V as a function of the time t.
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Chapter 5: Problem 67 Precalculus Enhanced with Graphing Utilities 6
The number N of cars produced at a certain factory in one day after t hours of operation is given by N(t) = 100t - 5t 2 , 0 t 10. If the cost C (in dollars) of producing N cars is C(N) = 15,000 + 8000N, find the cost C as a function of the time t of operation of the factory.
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Chapter 5: Problem 68 Precalculus Enhanced with Graphing Utilities 6
The number N of cars produced at a certain factory in one day after t hours of operation is given by N(t) = 100t - 5t 2 , 0 t 10. If the cost C (in dollars) of producing N cars is C(N) = 15,000 + 8000N, find the cost C as a function of the time t of operation of the factory.
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Chapter 5: Problem 69 Precalculus Enhanced with Graphing Utilities 6
The price p, in dollars, of a certain product and the quantity x sold obey the demand equation p = - 1 4 x + 100 0 x 400 Suppose that the cost C, in dollars, of producing x units is C = 1x 25 + 600 Assuming that all items produced are sold, find the cost C as a function of the price p.
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Chapter 5: Problem 70 Precalculus Enhanced with Graphing Utilities 6
The price p, in dollars, of a certain commodity and the quantity x sold obey the demand equation p = - 1 5 x + 200 0 x 1000 Suppose that the cost C, in dollars, of producing x units is C = 1x 10 + 400 Assuming that all items produced are sold, find the cost C as a function of the price p
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Chapter 5: Problem 71 Precalculus Enhanced with Graphing Utilities 6
The volume V of a right circular cylinder of height h and radius r is V = pr2 h. If the height is twice the radius, express the volume V as a function of r.
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Chapter 5: Problem 72 Precalculus Enhanced with Graphing Utilities 6
The volume V of a right circular cone is V = 1 3 pr2 h. If the height is twice the radius, express the volume V as a function of r.
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Chapter 5: Problem 73 Precalculus Enhanced with Graphing Utilities 6
Traders often buy foreign currency in hope of making money when the currencys value changes.
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Chapter 5: Problem 74 Precalculus Enhanced with Graphing Utilities 6
The function C1F2 = 5 9 1F - 322 converts a temperature in degrees Fahrenheit, F, to a temperature in degrees Celsius, C. The function K(C) = C + 273 converts a temperature in degrees Celsius to a temperature in kelvins, K. (a) Find a function that converts a temperature in degrees Fahrenheit to a temperature in kelvins. (b) Determine 80 degrees Fahrenheit in kelvins
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Chapter 5: Problem 75 Precalculus Enhanced with Graphing Utilities 6
The manufacturer of a computer is offering two discounts on last years model computer. The first discount is a $200 rebate and the second discount is 20% off the regular price, p. (a) Write a function f that represents the sale price if only the rebate applies. (b) Write a function g that represents the sale price if only the 20% discount applies. (c) Find f g and g f . What does each of these functions represent? Which combination of discounts represents a better deal for the consumer? Why?
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Chapter 5: Problem 76 Precalculus Enhanced with Graphing Utilities 6
If f and g are odd functions, show that the composite function f g is also odd.
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Chapter 5: Problem 77 Precalculus Enhanced with Graphing Utilities 6
If f is an odd function and g is an even function, show that the composite functions f g and g f are both even.
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