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Inverse Functions Section 1.8

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**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.

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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.

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**Vocabulary inverse function horizontal line test function composition**

one-to-one function

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**Given the functions and find each of the following:**

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**Determine if the function is one-to-one.**

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**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).

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**Find the inverse of the function**

Find the domains of the function and its inverse.

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**Find the inverse of the function**

Find the domains of the function and its inverse.

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**Find the inverse of the function**

Find the domains of the function and its inverse.

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**Find the inverse of the function**

Find the domains of the function and its inverse.

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

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**The function is not one-to-one**

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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