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: 9781319434526

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 4E (LL) W/ ACHIEVE ACCESS

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

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Prob. 33CRE Ch. 1 - Prob. 34CRE Ch. 1 - Prob. 35CRE Ch. 1 - Prob. 36CRE Ch. 1 - Prob. 37CRE Ch. 1 - Prob. 38CRE Ch. 1 - Prob. 39CRE Ch. 1 - Prob. 40CRE Ch. 1 - Prob. 41CRE Ch. 1 - Prob. 42CRE Ch. 1 - Prob. 43CRE Ch. 1 - Prob. 44CRE Ch. 1 - Prob. 45CRE Ch. 1 - Prob. 46CRE Ch. 1 - Prob. 47CRE Ch. 1 - Prob. 48CRE Ch. 1 - Prob. 49CRE Ch. 1 - Prob. 50CRE Ch. 1 - Prob. 51CRE Ch. 1 - Prob. 52CRE Ch. 1 - Prob. 53CRE Ch. 1 - Prob. 54CRE

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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