Explanation Given information: The function f ( x ) = ( 2 x − 1 ) − 3 / 2 Concept Used: The domain of a function is a set of input or argument values for which the function is defined. And value of a function f ( x ) at a point c is determined x = c by putting in that function. Calculation: To determine the domain of f ( x ) = ( 2 x − 1 ) − 3 / 2 , we have to look for the points where this function is defined. According to definition of a function, a function is defined where the function gives real value. In this case f ( x ) = ( 2 x − 1 ) − 3 / 2 = 1 ( 2 x − 1 ) 2 x − 1 This will be defined where 2 x − 1 > 0 since for 2 x − 1 = 0 the denominator of function will be zero and that will give undefined value, and for 2 x − 1 < 0 , 2 x − 1 will not give a real value. Thus, given function is defined 2 x − 1 > 0 thus where x > 1 2 . And the function will always give a real value for every real value greater than 1 2 . Now the maximum value that the function can take as input is ∞ whereas the minimum value that the function can take as input is 1 2 . So, domain of the given function is ( 1 2 , ∞ )

Calculus: Special Edition: Chapters 1-5 (w/ WebAssign)

6th Edition

ISBN: 9781524908102

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Chapter 1.4, Problem 5PS

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The domain of given function, and to find f(1),f(12),f(13) .

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Chapter 1.4, Problem 4PS

Chapter 1.4, Problem 6PS

Chapter 1 Solutions

Calculus: Special Edition: Chapters 1-5 (w/ WebAssign)

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The domain of given function, and to find f ( 1 ) , f ( 1 2 ) , f ( 13 ) .

Solution Summary: The author explains that a function is defined where the denominator of the function will be zero and that will give undefined value.

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The domain of given function, and to find f(1),f(12),f(13) .

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Chapter 1 Solutions