College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 6 - Section 6.2 - One-to-One Functions; Inverse Functions - 6.2 Assess Your Understanding - Page 423: 106

Answer

See below.

Work Step by Step

In a one-to-one function, for every $y=f(x)$there is a unique $x$. If it is not, then we cannot get a unique value for the inverse function (because there are more $x$s belonging to a $y$, whereas in a function, it must be unique). E.g. in the case of $x^2$, $f^{-1}(9)$ could be both $3$ and $-3$ , but it can only be one of them. However, there is no rule for us to decide which one of them to choose.
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