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Solved: Missing piece Let g(x)= x + 3 and find a function

Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett ISBN: 9780321570567 2

Solution for problem 44E Chapter 1.1

Calculus: Early Transcendentals | 1st Edition

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Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

Calculus: Early Transcendentals | 1st Edition

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Problem 44E

Missing? ?piece? ?Let g?(?x?)?= x? + 3 ?and find a function f that produces the given composition. (?g? °? ?? ?) ?= x?3?+3

Step-by-Step Solution:

Step-by-step solution Step 1 of 3 Step 2 of 3 The function (g f)(°)is the composite function and it can be written as g(f(x)), so we can write the following: (g f)(x) = g(f(x)) ° g(x) = x +3 2 g(f(x)) = f(x) +3…….(1) 2 From the text of the problem we have (g ° f)(x) = g(f(x)) = x +3, therefore based on the relation (1) we can write the following: f(x) +3 = x +3 3 Let’s rearrange this relation: 2 2 f(x) +3 = x +3 3 2 2 f(x) = x +333 2 2 f(x) = x 3 a b ab We will use the rule (x ) = x : 2 1 2 f(x) = (x ) 3 1 f(x) = x 3

Step 3 of 3

Chapter 1.1, Problem 44E is Solved
Textbook: Calculus: Early Transcendentals
Edition: 1
Author: William L. Briggs, Lyle Cochran, Bernard Gillett
ISBN: 9780321570567

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Solved: Missing piece Let g(x)= x + 3 and find a function

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