Explanation Given information : The given function is h ( x ) = ln ( x + 6 ) . Concept/definition used : A function f is a rule that assigns to each element x in a set D exactly one element, called f ( x ) , in a set E . The set D is called the domain of the function. The range of f is the set of all possible values of f ( x ) as x varies throughout the domain. Let f : A → B be a function then domain of the function f , D = A and the range R ⊆ E . Pictorial diagram of f : A → B is given here. Calculations: The given function is h ( x ) = ln ( x + 6 ) . The set of values of variable ‘ x’ for which function his defined is the domain. The function his defined for all x ∈ ℝ (set of real numbers) except when x + 6 ≤ 0 or x ≤ − 6 , i.e., for all real numbers x : − 6 < x the function h ( x ) is defined. Thus the domain of the function h ( x ) is the set − 6 < x , or the interval ( − 6 , ∞ )

15th Edition

ISBN: 9781133109631

Author: Stewart, JAMES, Day, Troy

Publisher: Cengage Learning,

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Chapter 1, Problem 9E

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Tofind:The domain and range of a function.

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Chapter 1, Problem 8E

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Tofind: The domain and range of a function.

Solution Summary: The author explains the domain and range of a function. The domain of the function is h(x) = -6x.

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