Inverse functions
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Inverse Functions . Section 1.8. Objectives. Determine if a function given as an equation is one-to-one. Determine if a function given as a graph is one-to-one. Algebraically find the inverse of a one-to-one function given as an equation.

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Inverse Functions

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Inverse functions

Inverse Functions

Section 1.8


Objectives

Objectives

  • Determine if a function given as an equation is one-to-one.

  • Determine if a function given as a graph is one-to-one.

  • Algebraically find the inverse of a one-to-one function given as an equation.

  • State the domain and range of a function and it inverse.


Objectives1

Objectives

  • State the relationships between the domain and range of a function and its inverse

  • Restrict the domain of a function that is not one-to-one so that an inverse function can be found.

  • Draw the graph of the inverse function given the graph of the function.


Vocabulary

Vocabulary

  • inverse function

  • horizontal line test

  • function composition

  • one-to-one function


Given the functions and find each of the following

Given the functions and find each of the following:


Determine if the function is one to one

Determine if the function is one-to-one.


Steps for finding an inverse function

Steps for finding an inverse function.

  • Change the function notation f(x) to y.

  • Change all the x’s to y’s and y’s to x’s.

  • Solve for y.

  • Replace y with f -1(x).


Find the inverse of the function

Find the inverse of the function

Find the domains of the function and its inverse.


Find the inverse of the function1

Find the inverse of the function

Find the domains of the function and its inverse.


Find the inverse of the function2

Find the inverse of the function

Find the domains of the function and its inverse.


Find the inverse of the function3

Find the inverse of the function

Find the domains of the function and its inverse.


Draw the graph of the inverse function for the graph of f x shown below

Draw the graph of the inverse function for the graph of f(x) shown below.


Inverse functions

The function is not one-to-one.  Choose the largest possible domain containing the number 100 so that the function restricted to the domain is one-to-one.  Find the inverse function for that restricted function.


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