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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find the domain
![### Mathematical Functions
In this section, we explore two multivariable functions, labeled (c) and (d).
#### Function (c)
\[
f(x, y, z) = \ln(x + y + z) + \frac{xyz}{\sqrt{x + y + z}}
\]
- **Description**: This function consists of two main components:
- The natural logarithm of the sum of the variables \(x\), \(y\), and \(z\).
- A fraction, where the numerator is the product of \(x\), \(y\), and \(z\), and the denominator is the square root of the sum of these variables.
#### Function (d)
\[
f(x, y, z) = \frac{e^{\sqrt{x+y+z}}}{z^2 - 1}
\]
- **Description**: This function involves:
- The exponential function raised to the power of the square root of the sum of \(x\), \(y\), and \(z\), forming the numerator.
- The denominator, which is \(z\) squared minus 1.
These functions illustrate complex interactions between exponential, logarithmic, and rational components, revealing deeper mathematical behaviors based on input values.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1079eff7-cd9f-4a9b-a6b7-8587fcd056cc%2F1b437318-1c96-4694-a1ce-a3a045c6279b%2Fl53r1lr_processed.png&w=3840&q=75)
Transcribed Image Text:### Mathematical Functions
In this section, we explore two multivariable functions, labeled (c) and (d).
#### Function (c)
\[
f(x, y, z) = \ln(x + y + z) + \frac{xyz}{\sqrt{x + y + z}}
\]
- **Description**: This function consists of two main components:
- The natural logarithm of the sum of the variables \(x\), \(y\), and \(z\).
- A fraction, where the numerator is the product of \(x\), \(y\), and \(z\), and the denominator is the square root of the sum of these variables.
#### Function (d)
\[
f(x, y, z) = \frac{e^{\sqrt{x+y+z}}}{z^2 - 1}
\]
- **Description**: This function involves:
- The exponential function raised to the power of the square root of the sum of \(x\), \(y\), and \(z\), forming the numerator.
- The denominator, which is \(z\) squared minus 1.
These functions illustrate complex interactions between exponential, logarithmic, and rational components, revealing deeper mathematical behaviors based on input values.
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