Explanation Given functions, f x = 2 x 2 - 5 x + 1 g x = 5 x + 1 The composite function f ∘ g is defined by, f ∘ g x = f g x The domain of f ∘ g consists of all those numbers in the domain of g for which g ( x ) is in the domain of f . Substituting g x = 5 x + 1 in the function f x = 2 x 2 - 5 x + 1 f ∘ g x = 2 ( 5 x + 1 ) 2 - 5 ( 5 x + 1 ) + 1 ( 5 x + 1 ) 2 can be expanded as 25 x 2 + 10 x + 1 Simplifying the above equation as below, f ∘ g x = 2 ( 25 x 2 + 10 x + 1 ) - 5 ( 5 x + 1 ) + 1 Multiplying the terms as indicated, f ∘ g x = 50 x 2 + 20 x + 2 - 25 x - 5 + 1 Rearranging the x -terms and constant terms as below,

12th Edition

ISBN: 9781305652231

Author: R. David Gustafson, Jeff Hughes

Publisher: Cengage Learning

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Chapter 3.CT, Problem 24CT

To determine

To find:

The value of (f∘g)(-1) where, fx=2x2-5x+1 and gx=5x+1.

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Chapter 3.CT, Problem 23CT

Chapter 3.CT, Problem 25CT

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