Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 1 - Section 1.5 - Inverse Functions and Logarithms - 1.5 Exercises: 33

Answer

(a) It is defined as the inverse function of the exponential function. (b) The domain of this function is $(0,\infty)$. (c) The range of this function is $(-\infty,\infty)$. (d) This shape is shown on the graph below.
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Work Step by Step

(a) It is defined as the inverse function of the exponential function i.e. as the solution of the equation $$a=b^x\Rightarrow x=\log_ba.$$ where $b$ is the basis for both the exponential function and the logarithm. (b) The domain of this function is the range of the exponential function i.e. the set of all positive reals $(0,\infty)$. (c) The range of this function is the domain of the exponential function i.e. it is the set of all reals $(-\infty,\infty)$. (d) This shape is obtained by reflecting the exponential function with $b>1$ about $x=y$ and it is shown on the figure bellow.
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