Explanation Given information : The function is f ( x ) = { x + 1 − 2 x − 6 i f x < − 3 i f | x | ≤ 3 i f x > 3 Formula/s used : Let f ( x ) : f : A → B is function defined for all x ∈ A , the set A is called the domain of the function f ( x ) . Calculations: The given function f ( x ) is union of three functions: f 1 ( x ) = x + 1 , i f x < − 3 , f 2 ( x ) = − 2 x i f | x | ≤ 3 , and f 3 ( x ) = − 6 , i f x > 3 . Therefore, the domain of function is the union of these three functions. Let D 1 be the domain of the function f 1 ( x ) = x + 1 , i f x < − 3 then D 1 is the interval D 1 = ( − ∞ , − 3 )

15th Edition

ISBN: 9781133109631

Author: Stewart, JAMES, Day, Troy

Publisher: Cengage Learning,

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Chapter 1.1, Problem 52E

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Tofind:The domain and sketch the graph of the function.

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Chapter 1.1, Problem 51E

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Tofind: The domain and sketch the graph of the function.

Solution Summary: The author calculates that the domain of the function f(x) is the union of three functions.

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Chapter 1 Solutions