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 - Page 416: 28



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) (red) is obtained by reflecting f(x) (blue) about the line y=x. The graph of $y=-\sqrt[3]{x+2}-8$ is obtained from g(x) by - shifting it left by $2$ units, - reflecting about the x axis (green) , and - shifting down by 8 units (black graph). This graph passes the Horizontal Line Test, so the function is one-to-one.
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