College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter 2 - Functions and Graphs - Exercise Set 2.6 - Page 297: 36

Answer

$f+g,f-g,fg$: all real numbers; $\frac{f}{g}$: all real numbers except $1$

Work Step by Step

For all but $\frac{f}{g}$, the domain includes all real numbers. To find the domain of $\frac{f}{g}$, set the denominator equal to $0$. $f+g=(6x^2-x-1)+(x-1)$ $f+g=6x^2-2$ $(-∞,∞)$ $f-g=(6x^2-x-1)-(x-1)$ $f-g=6x^2-2x$ $(-∞,∞)$ $fg=(6x^2-x-1)(x-1)$ $fg=6x^3-7x^2+1$ $(-∞,∞)$ $\frac{f}{g}=\frac{6x^2-x-1}{x-1}$ $x\ne1$
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