(a) Explanation Given information: f ( x ) = x 1 + x , g ( x ) = sin 2 x Calculation: Given that f ( x ) = x 1 + x and g ( x ) = sin 2 x Now ( f ∘ g ) ( x ) = f ( g ( x ) ) = f ( sin 2 x ) = sin 2 x 1 + sin 2 x Now sin 2 x 1 + sin 2 x is defined if and only if 1 + sin 2 x ≠ 0 , that is sin 2 x ≠ − 1 (b) To determine To find: g ∘ f and its domains. (c) To determine To find : f ∘ f and its domains. (d) To determine To find : g ∘ g and its domains.

15th Edition

ISBN: 9781133109631

Author: Stewart, JAMES, Day, Troy

Publisher: Cengage Learning,

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Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.

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Question

Chapter 1.3, Problem 34E

(a)

To determine

To find: f∘g and its domains.

(b)

To determine

To find: g∘f and its domains.

(c)

To determine

To find: f∘f and its domains.

(d)

To determine

To find: g∘g and its domains.

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Chapter 1.3, Problem 33E

Chapter 1.3, Problem 35E

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Chapter 1 Solutions

Biocalculus

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f ∘ g and its domains.

Solution Summary: The author explains how to find fcirc g and its domains.

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To find: f∘g and its domains.

To find: g∘f and its domains.

To find: f∘f and its domains.

To find: g∘g and its domains.

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Chapter 1 Solutions