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 )

7th Edition

ISBN: 9781524916817

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

Publisher: Kendall Hunt Publishing

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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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Chapter 1.5, Problem 10PS

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 9PS

Chapter 1.5, Problem 11PS

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Chapter 1 Solutions

Calculus

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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

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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 &lt; 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