Explanation Given information : The given function is g ( x ) = 16 − x 4 . 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 g ( x ) = 16 − x 4 . The set of values of variable ‘ x’ for which function gis defined is the domain. The function gis defined for all x ∈ ℝ (set of real numbers) except when 16 − x 4 <0 or x 4 > 16 ⇒ x > 2 , x < − 2 , i.e., for all real numbers x : − 2 ≤ x ≤ 2 the function g ( x ) is defined. Thus the domain of the function g ( x ) is the set − 2 ≤ x ≤ 2 , or the interval [ − 2 , 2 ]

15th Edition

ISBN: 9781133109631

Author: Stewart, JAMES, Day, Troy

Publisher: Cengage Learning,

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Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.

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Chapter 1, Problem 8E

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Tofind:The domain and range of a function.

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Chapter 1, Problem 7E

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Chapter 1 Solutions

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Tofind: The domain and range of a function.

Solution Summary: The author explains the function g(x) and its domain and range.

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