College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 5 - Section 5.2 - Properties of Rational Functions - 5.2 Assess Your Understanding: 21

Answer

Domain: All real numbers; $x \ne 2$

Work Step by Step

The domain of the function is all real numbers, except for when the denominator is 0. Thus, we let the denominator equal 0: $$ x^3 -8 =0\\(x-2)(x^2 +2x+4)=0\\ x = 2\\ $$ $\star$Note that $x^2 +2x+4$ will never equal 0. Thus, it does not restrict the domain of the function. Thus, we know that x cannot equal 2. Domain: All real numbers; $x \ne 2$
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