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 , ∞ )

4th Edition

ISBN: 9781319545956

Author: Rogawski

Publisher: MAC HIGHER

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topic…

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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

CALCULUS W/ACHIEVE PLATFORM

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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,∞)

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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,∞)