Explanation Concept used: Definition of inverse function: Consider f to be a one-to-one function with domain D and range R . Then its inverse function f − 1 has domain R and range D and it is defined as, f − 1 ( y ) = x ⇔ f ( x ) = y If the function f ( x ) is one-to-one, then it must satisfy the following condition. f ( x 1 ) = f ( x 2 ) ⇔ x 1 = x 2 To find the inverse of a function, first consider y = f ( x ) , then solve the equation for x in terms of y . Now, interchange x and y . Then resultant equation is given as, y = f − 1 ( x ) The term f − 1 ( x ) is called as the inverse function of f ( x ) . Given information: The linear function f ( x ) is, f ( x ) = m x + b Calculation: The given linear function f ( x ) is, f ( x ) = m x + b Now, check whether the function f ( x ) is one-to-one. Consider two numbers x 1 and x 2 such that f ( x 1 ) = f ( x 2 ) . Substitute x 1 for x in the function f ( x ) to obtain the value of f ( x 1 ) as, f ( x 1 ) = m x 1 + b Substitute x 2 for x in the function f ( x ) to obtain the value of f ( x 2 ) as, f ( x 2 ) = m x 2 + b Substitute ( m x 1 + b ) for f ( x 1 )

7th Edition

ISBN: 9781305115545

Author: James Stewart, Lothar Redlin, Saleem Watson

Publisher: Cengage Learning

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Chapter 2.8, Problem 102E

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The condition for the linear function f(x) to be linear and find its inverse if the linear function is one-to-one and check whether the inverse of the function f(x) is linear or not and also find its slope.

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The condition for the linear function f ( x ) to be linear and find its inverse if the linear function is one-to-one and check whether the inverse of the function f ( x ) is linear or not and also find its slope.

Solution Summary: The author explains the condition for the linear function f(x) to be one-to-one and its inverse.

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To find:

The condition for the linear function f(x) to be linear and find its inverse if the linear function is one-to-one and check whether the inverse of the function f(x) is linear or not and also find its slope.

Chapter 2 Solutions

The condition for the linear function f ( x ) to be linear and find its inverse if the linear function is one-to-one and check whether the inverse of the function f ( x ) is linear or not and also find its slope.

Solution Summary: The author explains the condition for the linear function f(x) to be one-to-one and its inverse.

Concept explainers

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To find: The condition for the linear function f(x) to be linear and find its inverse if the linear function is one-to-one and check whether the inverse of the function f(x) is linear or not and also find its slope.

Chapter 2 Solutions

To find:

The condition for the linear function f(x) to be linear and find its inverse if the linear function is one-to-one and check whether the inverse of the function f(x) is linear or not and also find its slope.