Explanation Given information: g ( x ) = { − x 2 when x < 0 x 2 when x ≥ 0 Concept used: One-to-One function:- A function f is one-to-one on a domain D if, for every value c, the equation f ( x ) = c has at most one solution for x ∈ D . Or, equivalently, if for all a , b ∈ D , if a ≠ b , then f ( a ) ≠ f ( b ) Inverse: - Let f have domain D and range R. If there is a function g with domain R such that g ( f ( x ) ) = x for x ∈ D and f ( g ( x ) ) = x for x ∈ R then f is said to be invertible. Calculation: g ( x ) = { − x 2 when x < 0 x 2 when x ≥ 0

4th Edition

ISBN: 9781319050740

Author: Jon Rogawski, Colin Adams, Robert Franzosa

Publisher: W. H. Freeman

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Chapter 1.5, Problem 28E

To determine

Find out whether the function g(x)={−x2 when x<0x2 when x≥0 is one-to-one, and if it is, determine the its inverse function.

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Chapter 1.5, Problem 27E

Chapter 1.5, Problem 29E

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Chapter 1 Solutions

Calculus: Early Transcendentals

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Find out whether the function g ( x ) = { − x 2 when x < 0 x 2 when x ≥ 0 is one-to-one, and if it is, determine the its inverse function.

Solution Summary: The author explains that if a function f is one-to-one, and determines its inverse function, it is invertible.

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Find out whether the function g(x)={−x2 when x<0x2 when x≥0 is one-to-one, and if it is, determine the its inverse function.

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Chapter 1 Solutions

Find out whether the function g ( x ) = { − x 2 when x &lt; 0 x 2 when x ≥ 0 is one-to-one, and if it is, determine the its inverse function.

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Find out whether the function g(x)={−x2 when x<0x2 when x≥0 is one-to-one, and if it is, determine the its inverse function.

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Chapter 1 Solutions

Find out whether the function g ( x ) = { − x 2 when x < 0 x 2 when x ≥ 0 is one-to-one, and if it is, determine the its inverse function.