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: 11

Answer

$(f+g)(x)=x^{2}-4x+5 \rightarrow$ $D=(-\infty,+\infty)$ $(f-g)(x)=-x^{2}+2x+5 \rightarrow$ $D=(-\infty,+\infty)$ $(f.g)(x)=-x^{3}+8x^{2}-15x \rightarrow$$D=(-\infty,+\infty)$ $(\frac{f}{g})(x)=\frac{5-x}{x^{2}-3x}\rightarrow$ $D=(-\infty,0)\cup(3,+\infty)$

Work Step by Step

We are given $f(x)=5-x$ and $g(x)=x^{2}-3x$ $(f+g)(x)=x^{2}-4x+5 \rightarrow$ $D=(-\infty,+\infty)$ $(f-g)(x)=-x^{2}+2x+5 \rightarrow$ $D=(-\infty,+\infty)$ $(f.g)(x)=(5-x)(x^{2}-3x)=5x^{2}-15x-x^{3}+3x^{2}=-x^{3}+8x^{2}-15x \rightarrow$$D=(-\infty,+\infty)$ $(\frac{f}{g})(x)=\frac{5-x}{x^{2}-3x}\rightarrow$ $D=(-\infty,0)\cup(3,+\infty)$
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