Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 4 - Inverse, Exponential, and Logarithmic Functions - 4.1 Inverse Functions - 4.1 Exercises: 27

Answer

one-to-one

Work Step by Step

$f(x)=x^{3}$ is a one-to-one function, and its inverse is $g(x)=\sqrt[3]{x},$(which is also one-to-one) The graph of g(x) is obtained by reflecting f(x) about the line y=x. The graph of $y=\sqrt[3]{x+1}-3$ is obtained from g(x) by - shifting it left by one unit, and - shifting down by three units. This graph passes the Horizontal Line Test, so the function is one-to-one
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