Explanation The given functionis f ( x ) = − x 2 − 4 x − 3 . As x ≤ − 2 the domain of the given function is negative numbers. x ≤ − 2 impliesthat the range of the given function is f ( x ) ≤ 1 . By the method of completing square rewrite the given function as, f ( x ) = − x 2 − 4 x − 3 = − ( x 2 + 4 x + 3 + 4 − 4 ) = − ( x 2 + 4 x + 4 − 1 ) = − ( x + 2 ) 2 + 1 Solve the function for x . y = − ( x + 2 ) 2 + 1 1 − y = ( x + 2 ) 2

Single Variable Calculus: Early Transcendentals (2nd Edition) - Standalone book

2nd Edition

ISBN: 9780321954237

Author: William L. Briggs, Lyle Cochran, Bernard Gillett

Publisher: PEARSON

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Chapter 1.3, Problem 38E

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To find: The inverse of f(x)=−x2−4x−3, for x≤−2 and express in the formof y=f−1(x); sketch the graph of f(x) and f−1(x).

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Chapter 1.3, Problem 37E

Chapter 1.3, Problem 39E

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Single Variable Calculus: Early Transcendentals (2nd Edition) - Standalone book

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The inverse of f ( x ) = − x 2 − 4 x − 3 , for x ≤ − 2 and express in the formof y = f − 1 ( x ) ; sketch the graph of f ( x ) and f − 1 ( x ) .

Solution Summary: The author illustrates the inverse of f(x)=-x

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To find: The inverse of f(x)=−x2−4x−3, for x≤−2 and express in the formof y=f−1(x); sketch the graph of f(x) and f−1(x).

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Chapter 1 Solutions