College Algebra (10th Edition)

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

Chapter 3 - Section 3.1 - Functions - 3.1 Assess Your Understanding - Page 211: 57


The domain of F(x) is {All real numbers, $x\ne0$}

Work Step by Step

$$F(x)= \frac{x-2}{x^{3}+x}$$ To find the domain, we first must find what values create a situation where the denominator equals 0. $${x^{3}+x}=0$$ $$x(x^{2}+1)=0 $$ $$x\ne0,x^{2}+1\ne0$$ If we solved for $x$ in $x^{2}+1\ne0$, it would give us an imaginary number. So, we just keep $x\ne0$, and use that for our domain.
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