Explanation Given information: Consider the polynomial f ( x ) with real coefficients having the property f ( g ( x ) ) = g ( f ( x ) ) for every polynomial g ( x ) with real coefficients. Calculation: Let g ( x ) be a constant function and hence it is given by g ( x ) = k , Where k is the constant. ∴ It is given by, f ( g ( x ) ) = f ( k ) . Form the above equation, we know that, g ( f ( x ) ) = k , since g ( x ) is a constant function

Student's Solution and Survival Manual for Calculus

7th Edition

ISBN: 9781524934040

Author: STRAUSS MONTY J, TODA MAGDALENA DANIELE, SMITH KARL J

Publisher: Kendall Hunt Publishing

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Concept explainers

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:

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Chapter 1, Problem 97SP

To determine

To calculate:The value of f(x) .

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Chapter 1, Problem 96SP

Chapter 1, Problem 98SP

Chapter 1 Solutions

Student's Solution and Survival Manual for Calculus

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Differential Equation | MIT 18.01SC Single Variable Calculus, Fall 2010; Author: MIT OpenCourseWare;https://www.youtube.com/watch?v=HaOHUfymsuk;License: Standard YouTube License, CC-BY

The value of f ( x ) .

Solution Summary: The author explains how to calculate the value of f(x).

Concept explainers

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To calculate:The value of f(x) .

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Chapter 1 Solutions