Explanation Given information: h ( t ) = ( t − 3 ) 2 Formula used: The Horizontal Line Test states that a function is one-to-one at the points at which a horizontal line will cross the function once at most. Therefore, we can only take half of the parabola h ( t ) = ( t − 3 ) 2 . Calculation: Consider the graph of h ( t ) = ( t − 3 ) 2 . Note that the Horizontal Line Test states that a function is one-to-one at the points at which a horizontal line will cross the function once at most. Therefore, we can only take half of the parabola h ( t ) = ( t − 3 ) 2 .Thus, h ( t ) is one-to-one on [ 3 , ∞ ) or ( − ∞ , 3 ] . For suppose we consider the domain as [ 3 , ∞ ) then y = h ( t ) = ( t − 3 ) 2 ( t ≥ 3 ) t − 3

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ISBN: 9781319050740

Author: Jon Rogawski, Colin Adams, Robert Franzosa

Publisher: W. H. Freeman

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Chapter 1, Problem 61CRE

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Find a domain on which h(t)=(t−3)2 is one to one and determine the inverse on this domain.

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Chapter 1, Problem 60CRE

Chapter 1, Problem 62CRE

Chapter 1 Solutions

Calculus: Early Transcendentals

Ch. 1.1 - Prob. 1PQ Ch. 1.1 - Prob. 2PQ Ch. 1.1 - Prob. 3PQ Ch. 1.1 - Prob. 4PQ Ch. 1.1 - Prob. 5PQ Ch. 1.1 - Prob. 6PQ Ch. 1.1 - Prob. 7PQ Ch. 1.1 - Prob. 8PQ Ch. 1.1 - Prob. 9PQ Ch. 1.1 - Prob. 10PQ

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Find a domain on which h ( t ) = ( t − 3 ) 2 is one to one and determine the inverse on this domain.

Solution Summary: The author explains that the Horizontal Line Test states that a function is one-to-one at the points at which the horizontal line will cross the function once at most.

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Find a domain on which h(t)=(t−3)2 is one to one and determine the inverse on this domain.

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Chapter 1 Solutions