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...
Related questions
Question
Find the x-values
![**Problem Statement:**
Determine the domain of the function \( f \).
\[
f(x) = 12x^3 + \frac{6}{x}
\]
**Options:**
A) \( x \neq 0 \)
B) \( x \neq 6 \)
C) \( (-\infty, \infty) \)
D) \( (0, \infty) \)
E) \( (-\infty, 0) \)
**Explanation:**
To find the domain of \( f(x) = 12x^3 + \frac{6}{x} \), we must identify the values of \( x \) for which the function is undefined. The term \(\frac{6}{x}\) signifies that the function is undefined when \( x = 0 \), as division by zero is undefined in mathematics. Therefore, the domain of the function is all real numbers except \( x = 0 \).
The correct answer is:
A) \( x \neq 0 \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7133a52f-2419-474e-98c9-6d24e97ee091%2F5e7f327c-497e-4665-83a6-380d8c0d301c%2Fb0xlec9_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Determine the domain of the function \( f \).
\[
f(x) = 12x^3 + \frac{6}{x}
\]
**Options:**
A) \( x \neq 0 \)
B) \( x \neq 6 \)
C) \( (-\infty, \infty) \)
D) \( (0, \infty) \)
E) \( (-\infty, 0) \)
**Explanation:**
To find the domain of \( f(x) = 12x^3 + \frac{6}{x} \), we must identify the values of \( x \) for which the function is undefined. The term \(\frac{6}{x}\) signifies that the function is undefined when \( x = 0 \), as division by zero is undefined in mathematics. Therefore, the domain of the function is all real numbers except \( x = 0 \).
The correct answer is:
A) \( x \neq 0 \)
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