Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 3 - Review Exercises - Page 512: 30

Answer

$\left.\begin{array}{ccc} & domain & range\\ \hline f(x) & (-\infty,\infty) & (0,\infty)\\ g(x) & (0,\infty) & (-\infty,\infty) \end{array}\right.$

Work Step by Step

$ f(x)=a^{x}$ and $ g(x)=\log_{a}x $ are inverse functions. Graphs of inverse functions are reflections of each other, over the line $ y=x.$ The graph of $2^{x}$ is always above the x-axis, rises from the far left slowly to pass through (0,1) on the y-axis, continues to rise through points $(1,2^{1}),(2,2^{2})$, etc. Plan: Plot some points $(x,2^{x})$ and join with a smooth curve to graph $ f(x).$ Graph the line $ y=x.$ Reflect the points plotted earlier about the line $ y=x.$ Join these new points to graph $ g(x)=\log_{2}x $ From the graph, read the domains and ranges, $\left.\begin{array}{ccc} & domain & range\\ \hline f(x) & (-\infty,\infty) & (0,\infty)\\ g(x) & (0,\infty) & (-\infty,\infty) \end{array}\right.$
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