Explanation Given: The given functions are f ( x ) = 5 x − 1 and g ( x ) = 3 x + 2 . Concept used: Take the value of g ( x ) as x and put it in the function f ( x ) . Calculation: Let us consider the functions f ( x ) = 5 x − 1 and g ( x ) = 3 x + 2 . Substitute 3 x + 2 for x in f ( x ) To determine (b) To find the function g ( f ( x ) ) . To determine (c) To find the function f ( f ( x ) ) .

6th Edition

ISBN: 9781119399353

Author: DA

Publisher: JOHN WILEY+SONS,INC.-CONSIGNMENT

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Concept explainers

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:

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Chapter 1.8, Problem 1P

To determine

(a)

To find the function f(g(x)).

To determine

(b)

To find the function g(f(x)).

To determine

(c)

To find the function f(f(x)).

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Chapter 1.7, Problem 54P

Chapter 1.8, Problem 2P

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u, v and w are three coplanar vectors: ⚫ w has a magnitude of 10 and points along the positive x-axis ⚫ v has a magnitude of 3 and makes an angle of 58 degrees to the positive x- axis ⚫ u has a magnitude of 5 and makes an angle of 119 degrees to the positive x- axis ⚫ vector v is located in between u and w a) Draw a diagram of the three vectors placed tail-to-tail at the origin of an x-y plane. b) If possible, find w × (ū+v) Support your answer mathematically or a with a written explanation. c) If possible, find v. (ū⋅w) Support your answer mathematically or a with a written explanation. d) If possible, find u. (vxw) Support your answer mathematically or a with a written explanation. Note: in this question you can work with the vectors in geometric form or convert them to algebraic vectors.

Question 3 (6 points) u, v and w are three coplanar vectors: ⚫ w has a magnitude of 10 and points along the positive x-axis ⚫ v has a magnitude of 3 and makes an angle of 58 degrees to the positive x- axis ⚫ u has a magnitude of 5 and makes an angle of 119 degrees to the positive x- axis ⚫ vector v is located in between u and w a) Draw a diagram of the three vectors placed tail-to-tail at the origin of an x-y plane. b) If possible, find w × (u + v) Support your answer mathematically or a with a written explanation. c) If possible, find v. (ū⋅ w) Support your answer mathematically or a with a written explanation. d) If possible, find u (v × w) Support your answer mathematically or a with a written explanation. Note: in this question you can work with the vectors in geometric form or convert them to algebraic vectors.

Chapter 1 Solutions

EBK APPLIED CALCULUS, ENHANCED ETEXT

Ch. 1.1 - Prob. 1P Ch. 1.1 - Prob. 2P Ch. 1.1 - Prob. 3P Ch. 1.1 - Prob. 4P Ch. 1.1 - Prob. 5P Ch. 1.1 - Prob. 6P Ch. 1.1 - Prob. 7P Ch. 1.1 - Prob. 8P Ch. 1.1 - Prob. 9P Ch. 1.1 - Prob. 10P

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(a) To find the function f ( g ( x ) ) .

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(a) To find the function f(g(x)).

(b) To find the function g(f(x)).

(c) To find the function f(f(x)).

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Chapter 1 Solutions

(a)

To find the function f(g(x)).

(b)

To find the function g(f(x)).

(c)

To find the function f(f(x)).