Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 1 - Section 1.5 - Inverse Functions and Logarithms - 1.5 Exercises: 1

Answer

a) A one-to-one function must: i) have one value for every input ii) not take the same value for different inputs ($f(x_{1})\ne f(x_{2})$) where $x_{1}\ne x_{2}$ b) Use the horizontal line test: a function is one-to-one if a horizontal line drawn to the graph only intersects the graph at one point.

Work Step by Step

a) The definition of a one-to-one function is a function (i) which never takes on the same value for different inputs (ii). b) A function is one-to-one if ii) is fulfilled. If ($f(x_{1})\ne f(x_{2})$) where $x_{1}\ne x_{2}$, the same y-value can not occur twice. The horizontal line test verifies this by checking whether the same y-value appears twice on the graph.
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