Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 6 - Inverse Functions - 6.2 Exponential Functions and Their Derivatives - 6.2 Exercises: 1

Answer

(a) $b^{x}=e^{xlnb}$ (b) $(-\infty,\infty)$ (c) $(0,\infty)$ (d) The general shape of the graph of the exponential function is as depicted in below figure.
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Work Step by Step

(a) The equation that defines $b^{x}$ when b is a positive number and x is a real number must be refers to $ b^{x}=e^{xlnb}$. (b) A function f is a rule that assigns to each element x in a set D exactly one element, called , in a set E. We usually consider functions for which the sets D and E are sets of real numbers. The set D is called the domain of the function. The domain for $f(x)=b^{x}(b>0)$ is for all real numbers. Hence, $(-\infty,\infty)$ (c) The number $f(x)=b^{x}$ is the value of f at x and is read “ f of x.” The range of f is the set of all possible values of as x varies throughout the domain. Hence, $(0,\infty)$ (d) The general shape of the graph of the exponential functions is as depicted in below figure.
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