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: 68


(a) $(f+g)(x)=5x-1$ (b) $(f-g(x)=-x+3$ (c) $(f . g)(x)=6x^2-x-2$ (d) $(\frac{f}{g})(x)=\frac{2x+1}{3x-2}$ The domain is {$x/x\ne\frac{2}{3}$} (e) $(f+g)(3)=14$ (f) $(f-g)(4)=-1$ (g) $(f . g)(2)=20$ (h) $(\frac{f}{g})(1)=3$

Work Step by Step

(a) $(f+g)(x)=$$f(x)+g(x)=2x+1+3x-2=5x-1$ (b) $(f-g)(x)=f(x)-g(x)=(2x+1)-(3x-2)=2x+1-3x+2=-x+3$ (c) $(f . g)(x)=f(x).g(x)=(2x+1)(3x-2)=6x^2-4x+3x-2=6x^2-x-2$ (d) $(\frac{f}{g})(x)=\frac{f(x)}{g(x)}=\frac{2x+1}{3x-2}$ The domain is {$x/x\ne\frac{2}{3}$} (e) $(f+g)(3)=$$f(3)+g(3)=5(3)-1=14$ (f) $(f-g)(4)=f(4)-g(4)=-4+3=-1$ (g) $(f . g)(2)=f(2).g(2)=6(2)^2-2-2=20$ (h) $(\frac{f}{g})(1)=\frac{f(1)}{g(1)}=\frac{2(1)+1}{3(1)-2}=3$
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