Explanation Given information: f ( x ) = x 2 x 2 − 1 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 To determine (b) If f ( x ) = x 2 x 2 − 1 then find the inverse function for f in [ 0 , ∞ )

Loose-Leaf Version for Calculus: Early Transcendentals Single Variable

4th Edition

ISBN: 9781319312886

Author: Rogawski, Jon, Adams, Colin, FRANZOSA, Robert

Publisher: W. H. Freeman

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Question

Chapter 1.5, Problem 57E

To determine

(a)

Let f(x)=x2x2−1 then explain why f is not invertible. Furthermore, explain why f is invertible if we restrict the domain to [0,∞).

To determine

(b)

If f(x)=x2x2−1 then find the inverse function for f in [0,∞)

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Chapter 1.5, Problem 56E

Chapter 1.5, Problem 58E

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Chapter 1 Solutions

Loose-Leaf Version for Calculus: Early Transcendentals Single Variable

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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(a) Let f ( x ) = x 2 x 2 − 1 then explain why f is not invertible. Furthermore, explain why f is invertible if we restrict the domain to [ 0 , ∞ ) .

Solution Summary: The author concludes that f is not one-to-one and therefore invertible.

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(a)

Let f(x)=x2x2−1 then explain why f is not invertible. Furthermore, explain why f is invertible if we restrict the domain to [0,∞).

(b)

If f(x)=x2x2−1 then find the inverse function for f in [0,∞)

Want to see the full answer?

Chapter 1 Solutions

(a) Let f ( x ) = x 2 x 2 − 1 then explain why f is not invertible. Furthermore, explain why f is invertible if we restrict the domain to [ 0 , ∞ ) .

Solution Summary: The author concludes that f is not one-to-one and therefore invertible.

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(a) Let f(x)=x2x2−1 then explain why f is not invertible. Furthermore, explain why f is invertible if we restrict the domain to [0,∞).

(b) If f(x)=x2x2−1 then find the inverse function for f in [0,∞)

Want to see the full answer?

Chapter 1 Solutions

(a)

Let f(x)=x2x2−1 then explain why f is not invertible. Furthermore, explain why f is invertible if we restrict the domain to [0,∞).

(b)

If f(x)=x2x2−1 then find the inverse function for f in [0,∞)