a. Explanation Definition used: “Given two functions f and g , the composite function, denoted by f ∘ g (read as “ f composed with g ”), is defined by ( f ∘ g ) ( x ) = f ( g ( x ) ) . The notation f ( g ( x ) ) is read f of g of x ”. Calculation: The given functions are f ( x ) = 3 x − 1 and g ( x ) = − 2 x + 5 . By using the above definition, find the value of the composite function ( f ∘ g ) ( x ) . ( f ∘ g ) ( x ) = f ( g ( x ) ) ( ∵ ( f ∘ g ) ( x ) = f ( b. To determine The composite function ( g ∘ f ) ( x ) for the given functions f ( x ) = 3 x − 1 and g ( x ) = − 2 x + 5 . c. To determine The composite function ( f ∘ f ) ( x ) for the given functions f ( x ) = 3 x − 1 and g ( x ) = − 2 x + 5 . d. To determine The composite function ( g ∘ g ) ( x ) for the given functions f ( x ) = 3 x − 1 and g ( x ) = − 2 x + 5 .

3rd Edition

ISBN: 9780321880116

Author: Michael Sullivan III, Katherine R. Struve, Janet Mazzarella

Publisher: PEARSON

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Chapter 11.1, Problem 28E

To determine

The composite function (f∘g)(x) for the given functions f(x)=3x−1 and g(x)=−2x+5.

To determine

The composite function (g∘f)(x) for the given functions f(x)=3x−1 and g(x)=−2x+5.

To determine

The composite function (f∘f)(x) for the given functions f(x)=3x−1 and g(x)=−2x+5.

To determine

The composite function (g∘g)(x) for the given functions f(x)=3x−1 and g(x)=−2x+5.

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Chapter 11.1, Problem 27E

Chapter 11.1, Problem 29E

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Chapter 11 Solutions

Elementary & Intermediate Algebra

Ch. 11.1 - Given two functions f and g, the ____ ____,...Ch. 11.1 - Prob. 2E Ch. 11.1 - Prob. 3E Ch. 11.1 - Prob. 4E Ch. 11.1 - Prob. 5E Ch. 11.1 - Prob. 6E Ch. 11.1 - Prob. 7E Ch. 11.1 - Prob. 8E Ch. 11.1 - Prob. 9E Ch. 11.1 - Prob. 10E

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The composite function ( f ∘ g ) ( x ) for the given functions f ( x ) = 3 x − 1 and g ( x ) = − 2 x + 5 .

Solution Summary: The author calculates the value of the composite function (fcirc g).

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The composite function (f∘g)(x) for the given functions f(x)=3x−1 and g(x)=−2x+5.

The composite function (g∘f)(x) for the given functions f(x)=3x−1 and g(x)=−2x+5.

The composite function (f∘f)(x) for the given functions f(x)=3x−1 and g(x)=−2x+5.

The composite function (g∘g)(x) for the given functions f(x)=3x−1 and g(x)=−2x+5.

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Chapter 11 Solutions