Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
What are the largest possible domains for the following functions: (a) f(x,y)= e√x+y (b) f(x, y) = log(x + √log(y)) (c) f(x, y, z)=√√xyz

What are the largest possible domains for the following functions: (a) f(x,y)= e√x+y (b) f(x, y) = log(x + √log(y)) (c) f(x, y, z)=√√xyz

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question
100%
**Title: Understanding the Largest Possible Domains for Given Functions** **Content:** To find the largest possible domains for the following functions, we need to consider the mathematical operations involved and the constraints they impose. **(a)** \( f(x, y) = e^{\sqrt{x+y}} \) - **Explanation:** The function involves an exponential function with an argument of a square root. The expression inside the square root, \( x + y \), must be non-negative for the square root to be defined in the real numbers. Therefore, the domain consists of all pairs \( (x, y) \) such that \( x + y \geq 0 \). **(b)** \( f(x, y) = \log(x + \sqrt{\log(y)}) \) - **Explanation:** This function involves a logarithm, which requires its argument to be positive. Therefore, \( x + \sqrt{\log(y)} > 0 \). Additionally, the argument inside the square root, \( \log(y) \), must be non-negative, which means \( y \) must be greater than or equal to 1. Thus, the domain consists of all pairs \( (x, y) \) where \( y \geq 1 \) and \( x + \sqrt{\log(y)} > 0 \). **(c)** \( f(x, y, z) = \sqrt{xyz} \) - **Explanation:** The function involves a square root, which requires its argument, \( xyz \), to be non-negative. Therefore, the domain includes all triples \( (x, y, z) \) such that \( xyz \geq 0 \). These domains ensure that the functions are well-defined in the realm of real numbers. Understanding these constraints helps in determining where each function operates without mathematical errors.
Transcribed Image Text:**Title: Understanding the Largest Possible Domains for Given Functions** **Content:** To find the largest possible domains for the following functions, we need to consider the mathematical operations involved and the constraints they impose. **(a)** \( f(x, y) = e^{\sqrt{x+y}} \) - **Explanation:** The function involves an exponential function with an argument of a square root. The expression inside the square root, \( x + y \), must be non-negative for the square root to be defined in the real numbers. Therefore, the domain consists of all pairs \( (x, y) \) such that \( x + y \geq 0 \). **(b)** \( f(x, y) = \log(x + \sqrt{\log(y)}) \) - **Explanation:** This function involves a logarithm, which requires its argument to be positive. Therefore, \( x + \sqrt{\log(y)} > 0 \). Additionally, the argument inside the square root, \( \log(y) \), must be non-negative, which means \( y \) must be greater than or equal to 1. Thus, the domain consists of all pairs \( (x, y) \) where \( y \geq 1 \) and \( x + \sqrt{\log(y)} > 0 \). **(c)** \( f(x, y, z) = \sqrt{xyz} \) - **Explanation:** The function involves a square root, which requires its argument, \( xyz \), to be non-negative. Therefore, the domain includes all triples \( (x, y, z) \) such that \( xyz \geq 0 \). These domains ensure that the functions are well-defined in the realm of real numbers. Understanding these constraints helps in determining where each function operates without mathematical errors.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS