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 417: 37



Work Step by Step

See: Important Facts about Inverses, p.414, 1. If $f$ is one-to-one, then $f^{-1}$ exists. 2. The domain of $f$ is the range of $f^{-1}$, and the range of $f$ is the domain of $f^{-1}$. 3. If the point $(a, b)$ lies on the graph of $f$, then $(b, a)$ lies on the graph of $f^{-1}$. ------------------- $(3,-4)$ is on the graph of f, $(-4,3) $ is on the graph of g, $(2,-6)$ is on the graph of f, $(-6,2) $ is on the graph of g, $(5,8)\quad\leftrightarrow\quad (8,5)$ $(1,9)\quad\leftrightarrow\quad (9,1)$ $(4,8)\quad\leftrightarrow\quad (3,4)$ ... valid for all five pairs (x,f(x)), so yes, they are inverses.
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