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: 9781319379421

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 1.5, Problem 28E

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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 1.5, Problem 27E

Chapter 1.5, Problem 29E

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Chapter 1 Solutions

CALCULUS 4E (HC) W/ ACHIEVE ACCESS

Ch. 1.1 - Prob. 1PQ Ch. 1.1 - Prob. 2PQ Ch. 1.1 - Prob. 3PQ Ch. 1.1 - Prob. 4PQ Ch. 1.1 - Prob. 5PQ Ch. 1.1 - Prob. 6PQ Ch. 1.1 - Prob. 7PQ Ch. 1.1 - Prob. 8PQ Ch. 1.1 - Prob. 9PQ Ch. 1.1 - Prob. 10PQ

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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

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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.