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Find the Domain and Range of the following Function f (x) = e3r-7 +1 %3D

Find the Domain and Range of the following Function f (x) = e3r-7 +1 %3D

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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**Question 8** Find the Domain and Range of the following function: \[ f(x) = e^{3x - 7} + 1 \] **Explanation:** - **Domain**: The domain of a function is the set of all possible input values (x-values) that the function can accept. For the function \( f(x) = e^{3x - 7} + 1 \), there are no restrictions on the value of \( x \). Therefore, the domain is all real numbers. - **Range**: The range is the set of all possible output values (y-values) of the function. Since the exponential function \( e^{3x - 7} \) is always positive, the smallest value it approaches is 0 (as \( x \) approaches negative infinity). Thus, \( e^{3x - 7} + 1 \) will always be greater than 1. Therefore, the range of the function is \( (1, \infty) \).
Transcribed Image Text:**Question 8** Find the Domain and Range of the following function: \[ f(x) = e^{3x - 7} + 1 \] **Explanation:** - **Domain**: The domain of a function is the set of all possible input values (x-values) that the function can accept. For the function \( f(x) = e^{3x - 7} + 1 \), there are no restrictions on the value of \( x \). Therefore, the domain is all real numbers. - **Range**: The range is the set of all possible output values (y-values) of the function. Since the exponential function \( e^{3x - 7} \) is always positive, the smallest value it approaches is 0 (as \( x \) approaches negative infinity). Thus, \( e^{3x - 7} + 1 \) will always be greater than 1. Therefore, the range of the function is \( (1, \infty) \).
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