Explanation Given: The functions f ( x ) = x and g ( x ) = x + 1 . Key concepts used: Composition of two functions is defined as: ⇒ f ∘ g ( x ) = f ( g ( x ) ) ⇒ g ∘ f ( x ) = g ( f ( x ) ) While finding domain of a composite function, restrictions on the composite function as well as restrictions on inner function are taken into account. Calculation: First of all, we find composite functions as shown below: ⇒ f ∘ g ( x ) = f ( g ( x ) ) ⇒ f ∘ g ( x ) = f ( x + 1 ) ⇒ f ∘ g ( x ) = x + 1 Domain of square root function can be found by setting its argument greater than or equal to zero. ⇒ x + 1 ≥ 0 ⇒ x + 1 − 1 ≥ 0 − 1 ⇒ x ≥ − 1 Inner function g ( x ) = x + 1 is a linear function and is defined for all the values of x

4th Edition

ISBN: 9781319434540

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 1.3, Problem 25E

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Composite functions f∘g and g∘f and their domains.

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Chapter 1.3, Problem 24E

Chapter 1.3, Problem 26E

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Chapter 1 Solutions

ACHIEVE STANDALONE ACCESS F/ CALC 4E

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Composite functions f ∘ g and g ∘ f and their domains.

Solution Summary: The author explains how to determine composite functions and their domains. The domain of a square root function can be found by setting its argument greater than or equal to zero.

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Composite functions f∘g and g∘f and their domains.

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Chapter 1 Solutions