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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Can you please explain how to find the domain and for what values is the function increasing and decreasing
![### Function Definition
Given:
\[ \text{Let } f(x) = x - 3 \sqrt[3]{x} \]
### Explanation
- \( f(x) \) represents a function of \( x \).
- \( x \) is the input variable.
- The function subtracts three times the cube root of \( x \) from \( x \).
### Mathematical Representation
\[ f(x) = x - 3 \sqrt[3]{x} \]
Where:
- \( x \) is any real number.
- \( 3 \sqrt[3]{x} \) represents three times the cube root of \( x \).
This function combines linear and radical components to create a unique mathematical relationship. The function can be analyzed graphically by plotting \( f(x) \) against \( x \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F357de21d-4dd5-43e5-ad45-c8ac77f9a858%2Fb9904376-8274-4295-ac0c-e48054b684ee%2F9s032og_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Function Definition
Given:
\[ \text{Let } f(x) = x - 3 \sqrt[3]{x} \]
### Explanation
- \( f(x) \) represents a function of \( x \).
- \( x \) is the input variable.
- The function subtracts three times the cube root of \( x \) from \( x \).
### Mathematical Representation
\[ f(x) = x - 3 \sqrt[3]{x} \]
Where:
- \( x \) is any real number.
- \( 3 \sqrt[3]{x} \) represents three times the cube root of \( x \).
This function combines linear and radical components to create a unique mathematical relationship. The function can be analyzed graphically by plotting \( f(x) \) against \( x \).
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