Precalculus: Mathematics for Calculus - 6th Edition
Precalculus: Mathematics for Calculus - 6th Edition
6th Edition
ISBN: 9780840068071
Author: Stewart, James, Redlin, Lothar, Watson, Saleem
Publisher: Cengage Learning
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Chapter 2, Problem 20RE
To determine

Find the domain of the function f(x)=2x2+5x+32x2−5x−3

Expert Solution & Answer
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Answer to Problem 20RE

The domain of the function,

  f(x)=2x2+5x+32x2−5x−3 is [(−∞,−1.5)∪(−1.5,−1)∪(−1,−0.5)∪(−0.5,3)∪(3,∞)]

Explanation of Solution

Given information: Consider the function f(x)=2x2+5x+32x2−5x−3

Calculation:

For Numerator,

A rational expression is not defined when the denominator is 0.

Since ,

  2x2+5x+3≠0⇒2x2+2x+3x+3≠0⇒2x(x+1)+3(x+1)≠0⇒(2x+3)(x+1)≠0

Then,

  x+1≠0⇒x≠−1 and

Hence the Numerator in the given function is defined for all the values of x in the set of real numbers except of the values at x=−1.5 and x=−1 .

And for denominator,

A rational expression is not defined when the denominator is 0.

Since

  2x+1≠0⇒2x≠−1⇒x≠−12⇒x≠−0.5 Then,

and

Hence the Denominator in the given function is defined for all the values of x in the set of real numbers except of the values at x=−0.5 and x=3 .

Thus, the domain of the function,

  f(x)=2x2+5x+32x2−5x−3 is [(−∞,−1.5)∪(−1.5,−1)∪(−1,−0.5)∪(−0.5,3)∪(3,∞)]

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Chapter 2, Problem 19RE
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Chapter 2 Solutions

Precalculus: Mathematics for Calculus - 6th Edition

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Prob. 49ECh. 2.5 - Prob. 50ECh. 2.5 - Prob. 51ECh. 2.5 - Prob. 52ECh. 2.5 - Prob. 53ECh. 2.5 - Prob. 54ECh. 2.5 - Prob. 55ECh. 2.5 - Prob. 56ECh. 2.5 - Prob. 57ECh. 2.5 - Prob. 58ECh. 2.5 - Prob. 59ECh. 2.5 - Prob. 60ECh. 2.5 - Prob. 61ECh. 2.5 - Prob. 62ECh. 2.5 - Prob. 63ECh. 2.5 - Prob. 64ECh. 2.5 - Prob. 65ECh. 2.5 - Prob. 66ECh. 2.5 - Prob. 67ECh. 2.5 - Prob. 68ECh. 2.5 - Prob. 69ECh. 2.5 - Prob. 70ECh. 2.5 - Prob. 71ECh. 2.5 - Prob. 72ECh. 2.5 - Prob. 73ECh. 2.5 - Prob. 74ECh. 2.5 - Prob. 75ECh. 2.5 - Prob. 76ECh. 2.5 - Prob. 77ECh. 2.5 - Prob. 78ECh. 2.5 - Prob. 79ECh. 2.5 - Prob. 80ECh. 2.5 - Prob. 81ECh. 2.5 - Prob. 82ECh. 2.5 - Prob. 83ECh. 2.5 - Prob. 84ECh. 2.5 - Prob. 85ECh. 2.5 - Prob. 86ECh. 2.5 - Prob. 87ECh. 2.5 - Prob. 88ECh. 2.5 - Prob. 89ECh. 2.5 - Prob. 90ECh. 2.5 - Prob. 91ECh. 2.5 - Prob. 92ECh. 2.5 - Prob. 93ECh. 2.6 - From the graphs of f and g in the figure, we find...Ch. 2.6 - By definition, (f g)(x) = _____. 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Find a...Ch. 2 - Prob. 19PCh. 2 - Minimizing a Sum Find two positive numbers whose...Ch. 2 - Prob. 21PCh. 2 - Dividing a Pen A rancher with 750 ft of fencing...Ch. 2 - Fencing a Garden Plot A property owner wants to...Ch. 2 - Maximizing Area A wire 10 cm long is cut into two...Ch. 2 - Light from a Window A Norman window has the shape...Ch. 2 - Volume of a Box A box with an open top is to be...Ch. 2 - Area of a Box An open box with a square base is to...Ch. 2 - Inscribed Rectangle Find the dimensions that give...Ch. 2 - Minimizing Costs A rancher wants to build a...Ch. 2 - Minimizing Time A man stands at a point A on the...Ch. 2 - Bird Flight A bird is released from point A on an...Ch. 2 - Area of a Kite A kite frame is to be made from six...
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