Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 2 - Section 2.3 - The Algebra of Functions - Exercise Set - Page 132: 17

Answer

The answers are $ (f+g)(x) = 3x-3 $ $ (f-g)(x)=7x+3 $ $ (fg)(x)= -10x^2-15x $ $ \left (\frac{f}{g} \right )(x) = \frac {5x}{-2x-3} $

Work Step by Step

Given functions are $ f(x)=5x $ and $ g(x)=-2x-3 $ $ (f+g)(x) = f(x)+g(x) $ Substitute values. $ (f+g)(x) = 5x-2x-3 $ $ (f+g)(x) = 3x-3 $ $ (f-g)(x) = f(x)-g(x) $ Substitute values. $ (f-g)(x)=5x-(-2x-3) $ $ (f-g)(x)=5x+2x+3 $ $ (f-g)(x)=7x+3 $ $ (fg)(x)=f(x)\times g(x) $ Substitute values. $ (fg)(x)=(5x) \times (-2x-3) $ $ (fg)(x)= -10x^2-15x $ $ \left (\frac{f}{g} \right )(x) = \frac {f(x)}{g(x)} $ Substitute values. $ \left (\frac{f}{g} \right )(x) = \frac {5x}{-2x-3} $ .
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