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1. Find and describe the domain of the following functions a) f(x,y) = In(x² + 4y² – 4) b) g(x,y, z) = V4 – x² – y² – z²

1. Find and describe the domain of the following functions a) f(x,y) = In(x² + 4y² – 4) b) g(x,y, z) = V4 – x² – y² – z²

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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## Problem Statement 1. Find and describe the domain of the following functions: a) \( f(x, y) = \ln(x^2 + 4y^2 - 4) \) b) \( g(x, y, z) = \sqrt{4 - x^2 - y^2 - z^2} \) --- ### Explanation: - **Function a**: - The function \( f(x, y) = \ln(x^2 + 4y^2 - 4) \) requires the input to the natural logarithm to be greater than zero. Thus, the domain of the function is the set of all \((x, y)\) such that \( x^2 + 4y^2 - 4 > 0 \). - **Function b**: - The function \( g(x, y, z) = \sqrt{4 - x^2 - y^2 - z^2} \) requires the expression under the square root to be non-negative. Therefore, the domain consists of all \((x, y, z)\) such that \( 4 - x^2 - y^2 - z^2 \geq 0 \).
Transcribed Image Text:## Problem Statement 1. Find and describe the domain of the following functions: a) \( f(x, y) = \ln(x^2 + 4y^2 - 4) \) b) \( g(x, y, z) = \sqrt{4 - x^2 - y^2 - z^2} \) --- ### Explanation: - **Function a**: - The function \( f(x, y) = \ln(x^2 + 4y^2 - 4) \) requires the input to the natural logarithm to be greater than zero. Thus, the domain of the function is the set of all \((x, y)\) such that \( x^2 + 4y^2 - 4 > 0 \). - **Function b**: - The function \( g(x, y, z) = \sqrt{4 - x^2 - y^2 - z^2} \) requires the expression under the square root to be non-negative. Therefore, the domain consists of all \((x, y, z)\) such that \( 4 - x^2 - y^2 - z^2 \geq 0 \).
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