Explanation Given: The function f ( x ) = x + 1 x 2 + 2 c x + 4 Key concepts used: Domain of a rational function is all real numbers expect the values of x that make the denominator zero. Discriminant of a quadratic equation a x 2 + b x + c = 0 is given by D = b 2 − 4 a c Calculation: For the domain of the function f ( x ) = x + 1 x 2 + 2 c x + 4 to be all real numbers, the denominator mustn’t have any solutions. Therefore, the equation x 2 + 2 c x + 4 = 0 must not have any solutions. That will be possible if discriminant of this quadratic equation is negative

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Question

Chapter 1.3, Problem 40E

To determine

To prove:

The values of c such that the given function has domain all real numbers.

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Chapter 1.3, Problem 39E

Chapter 1.3, Problem 41E

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Chapter 1 Solutions

Calculus - Standalone book

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To prove: The values of c such that the given function has domain all real numbers.

Solution Summary: The author explains the required set of values of c for which domain of the function f(x)=x +2cx+4 is all real numbers.