College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 2, Functions - Section 2.7 - Combining Functions - 2.7 Exercises - Page 252: 10


$(f+g)(x)=-1 \rightarrow$ $D=(-\infty,+\infty)$ $(f-g)(x)=7 -2x^{2} \rightarrow$ $D=(-\infty,+\infty)$ $(f.g)(x)=3x^{2}-12 -x^{4}+4x^{2} = 4x^{2}-x^{4}-12\rightarrow$ $D=(-\infty,+\infty)$ $(\frac{f}{g})(x)=\frac{3-x^{2}}{x^{2}-4}\rightarrow$ $D=(-\infty,-2)\cup(2,+\infty)$

Work Step by Step

We are given $f(x)=3-x^{2}$ and $g(x)=x^{2}-4$ $(f+g)(x)=-1 \rightarrow$ the domain is $(-\infty,+\infty)$ $(f-g)(x)=7 -2x^{2} \rightarrow$ the domain is $(-\infty,+\infty)$ $(f.g)(x)=3x^{2}-12 -x^{4}+4x^{2} = 4x^{2}-x^{4}-12\rightarrow$ the domain is $(-\infty,+\infty)$ $(\frac{f}{g})(x)=\frac{3-x^{2}}{x^{2}-4}\rightarrow$ the domain is $(-\infty,-2)\cup(2,+\infty)$
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