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# Inverse Functions PowerPoint PPT Presentation

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

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.

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

### 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

• inverse function

• horizontal line test

• function composition

• one-to-one 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 domains of the function and its inverse.

### Find the inverse of the function

Find the domains of the function and its inverse.

### Find the inverse of the function

Find the domains of the function and its inverse.

### 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.

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.