Explanation Given information: f ( x ) = x 2 , x > 0 ; g ( x ) = − x , x > 0 Concept Used: Let f and g are the functions with domain D 1 and D 2 respectively, and range D 2 and D 1 respectively. Then these functions are inverses of each other if g [ f ( x ) ] = x for all x in D 1 And f [ g ( x ) ] = x for all x in D 2 Calculation: In order to determine if the functions f ( x )

Student's Solution and Survival Manual for Calculus

7th Edition

ISBN: 9781524934040

Author: STRAUSS MONTY J, TODA MAGDALENA DANIELE, SMITH KARL J

Publisher: Kendall Hunt Publishing

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Concept explainers

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:

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Question

Chapter 1.5, Problem 9PS

To determine

To find if the functions

f(x)=x2,x>0;g(x)=−x,x>0

are inverses of each other.

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Chapter 1.5, Problem 8PS

Chapter 1.5, Problem 10PS

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Chapter 1 Solutions

Student's Solution and Survival Manual for Calculus

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

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To find if the functions f ( x ) = x 2 , x > 0 ; g ( x ) = − x , x > 0 are inverses of each other.

Solution Summary: The author explains that given functions f and g are not inverses of each other.

Concept explainers

Videos

To find if the functions

f(x)=x2,x>0;g(x)=−x,x>0

are inverses of each other.

Want to see the full answer?

Chapter 1 Solutions

To find if the functions f ( x ) = x 2 , x &gt; 0 ; g ( x ) = − x , x &gt; 0 are inverses of each other.

Solution Summary: The author explains that given functions f and g are not inverses of each other.

Concept explainers

Videos

To find if the functions f(x)=x2,x>0;g(x)=−x,x>0 are inverses of each other.

Want to see the full answer?

Chapter 1 Solutions

To find if the functions f ( x ) = x 2 , x > 0 ; g ( x ) = − x , x > 0 are inverses of each other.

To find if the functions

f(x)=x2,x>0;g(x)=−x,x>0

are inverses of each other.