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 - Page 418: 1


(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.

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.
Small 1519426270
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.