Explanation Given: The functions f ( x ) = 1 x and g ( x ) = x − 4 . 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 − 4 ) ⇒ f ∘ g ( x ) = 1 x − 4 ⇒ f ∘ g ( x ) = x 4 This is a polynomial, so there are no restrictions on it. Inner function g ( x ) = x − 4 = 1 x 4 has a restriction x ≠ 0 . Thus, domain of the function f ∘ g ( x ) is ( − ∞ , 0 ) ∪ ( 0 , ∞ )

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ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 1.3, Problem 26E

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

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Chapter 1.3, Problem 25E

Chapter 1.3, Problem 27E

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Chapter 1 Solutions

CALCULUS (CLOTH)

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

Ch. 1.1 - Prob. 1E Ch. 1.1 - Prob. 2E Ch. 1.1 - Prob. 3E Ch. 1.1 - Prob. 4E Ch. 1.1 - Prob. 5E Ch. 1.1 - Prob. 6E Ch. 1.1 - Prob. 7E Ch. 1.1 - Prob. 8E Ch. 1.1 - Prob. 9E Ch. 1.1 - Prob. 10E Ch. 1.1 - Prob. 11E Ch. 1.1 - Prob. 12E Ch. 1.1 - Prob. 13E Ch. 1.1 - Prob. 14E Ch. 1.1 - Prob. 15E Ch. 1.1 - Prob. 16E Ch. 1.1 - Prob. 17E Ch. 1.1 - Prob. 18E Ch. 1.1 - Prob. 19E Ch. 1.1 - Prob. 20E Ch. 1.1 - Prob. 21E Ch. 1.1 - Prob. 22E Ch. 1.1 - Prob. 23E Ch. 1.1 - Prob. 24E Ch. 1.1 - Prob. 25E Ch. 1.1 - Prob. 26E Ch. 1.1 - Prob. 27E Ch. 1.1 - Prob. 28E Ch. 1.1 - Prob. 29E Ch. 1.1 - Prob. 30E Ch. 1.1 - Prob. 31E Ch. 1.1 - Prob. 32E Ch. 1.1 - Prob. 33E Ch. 1.1 - Prob. 34E Ch. 1.1 - Prob. 35E Ch. 1.1 - Prob. 36E Ch. 1.1 - Prob. 37E Ch. 1.1 - Prob. 38E Ch. 1.1 - Prob. 39E Ch. 1.1 - Prob. 40E Ch. 1.1 - Prob. 41E Ch. 1.1 - Prob. 42E Ch. 1.1 - Prob. 43E Ch. 1.1 - Prob. 44E Ch. 1.1 - Prob. 45E Ch. 1.1 - Prob. 46E Ch. 1.1 - Prob. 47E Ch. 1.1 - Prob. 48E Ch. 1.1 - Prob. 49E Ch. 1.1 - Prob. 50E Ch. 1.1 - 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Composite functions f ∘ g and g ∘ f and their domains.

Solution Summary: The author explains the composition of two functions: fcirc g(x)=x

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

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Chapter 1 Solutions