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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Question
![The expression from the image is part of a mathematical function. It is denoted as:
\[
(b) \quad f(x) = \tan^{-1}(5x) \cdot (\ln(2^x))^6
\]
Explanation:
- \(\tan^{-1}(5x)\) refers to the inverse tangent (or arctangent) function applied to \(5x\).
- \(\ln(2^x)\) is the natural logarithm of \(2\) raised to the power of \(x\).
- The logarithmic expression is then raised to the sixth power, denoted by \((\ln(2^x))^6\).
This function demonstrates the composition of inverse trigonometric and logarithmic expressions, useful in calculus and analysis.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F108ede44-c850-4a94-924c-e890d79e0463%2F8fd72a57-c4f6-4149-b717-7f54d603ed08%2F9l2gz5f_processed.png&w=3840&q=75)
Transcribed Image Text:The expression from the image is part of a mathematical function. It is denoted as:
\[
(b) \quad f(x) = \tan^{-1}(5x) \cdot (\ln(2^x))^6
\]
Explanation:
- \(\tan^{-1}(5x)\) refers to the inverse tangent (or arctangent) function applied to \(5x\).
- \(\ln(2^x)\) is the natural logarithm of \(2\) raised to the power of \(x\).
- The logarithmic expression is then raised to the sixth power, denoted by \((\ln(2^x))^6\).
This function demonstrates the composition of inverse trigonometric and logarithmic expressions, useful in calculus and analysis.
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