# Solved: 2 Missing piece et g ) x + 3 a nd find a function ## Problem 42E Chapter 1.1

Calculus: Early Transcendentals | 1st Edition

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Problem 42E

2? Missing? ?piece ? ? ? et g?? )? x + 3 a ? nd find a function f that produces the given composition. 4? 2? ? ? ? (?f ° ? )(? ) ? ? x + 6x ? + 20

Step-by-Step Solution:

Step-by-step solution Step 1 of 3 Step 2 of 3 The function (f g)°x)is the composite function and it can be written as f(g(x)), so we can write the following: (f °)(x) = f(g(x)) 2 = f(x + 3) = x + 6x + 20 We cannot apply directly the rule for the square of binomial so we will rearrange this function: (f g)(x) = x + 6x + 20 ° = x + 6x + 9 + 11 2 If we write x and 9 as (x ) and 3 then we can apply the rule for the square of binomial (a + b) = a + 2ab + b : 2 4 2 (f °)(x) = x + 6x + 9 + 11 2 2 2 2 = (x ) + 2 · x · 3 + 3 + 11 2 2 = (x + 3) + 11 Suppose x + 3 = y then f(y) = x + 6x + 9 + 11 = (x + 3) + 11 = y + 11 2 Thus the required function is f(x) = x + 11

Step 3 of 3

##### ISBN: 9780321570567

Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567. This full solution covers the following key subjects: composition, Find, function, given, missing. This expansive textbook survival guide covers 85 chapters, and 5218 solutions. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1. The full step-by-step solution to problem: 42E from chapter: 1.1 was answered by , our top Calculus solution expert on 03/03/17, 03:45PM. Since the solution to 42E from 1.1 chapter was answered, more than 269 students have viewed the full step-by-step answer. The answer to “2? Missing? ?piece ? ? ? et g?? )? x + 3 a ? nd find a function f that produces the given composition. 4? 2? ? ? ? (?f ° ? )(? ) ? ? x + 6x ? + 20” is broken down into a number of easy to follow steps, and 42 words.

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