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How do I find the inverse of functions?

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4.3 Use Inverse Functions Inverse Functions Functions f and g are inverse functions of each other provided: The function g is denoted by f 1, read as “f inverse.”

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4.3 Use Inverse Functions Horizontal Line Test The inverse of a function f is also a function if and only if no horizontal line intersects the graph of f _______ __________. more than once Function Not a Function

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4.3 Use Inverse Functions Example 1 Verify that functions are inverses

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4.3 Use Inverse Functions Example 1 Verify that functions are inverses

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4.3 Use Inverse Functions Checkpoint. Find the inverse of the function. Then verify that your result and the original functions are inverses.

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4.3 Use Inverse Functions Example 2 Find the inverse of a function of the form a Consider the function Determine whether the inverse of f is a function. Then find the inverse. Graph the function. Notice that no horizontal line intersects the graph more than once. The inverse of f is a function. To find an equation for f, complete the following steps. Replace f (x) with y.

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4.3 Use Inverse Functions Example 2 Find the inverse of a function of the form a Consider the function Determine whether the inverse of f is a function. Then find the inverse. Replace f (x) with y. Switch x and y. Multiply each side by y. Divide each side by x. The inverse of f is f 1 (x) = _____.

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4.3 Use Inverse Functions Checkpoint. Complete the following exercise.

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4.3 Use Inverse Functions Example 3 Find the inverse of a quadratic function Find the inverse of Then graph f and f – 1. Write original function. Replace f (x) with y. Switch x with y. Divide each side by 4. Take square roots of each side.

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4.3 Use Inverse Functions Example 3 Find the inverse of a quadratic function Find the inverse of Then graph f and f – 1. The domain of f is restricted to negative values of x. So, the range of f must be restricted to negative values, and therefore the inverse is f 1 ( x ) = ______. (If the domain were restricted to x > 0, you would choose f 1 ( x ) = ______. )

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4.3 Use Inverse Functions Checkpoint. Complete the following exercise.

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4.3 Use Inverse Functions Checkpoint. Find the inverse of the function.

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4.3 Use Inverse Functions Checkpoint. Find the inverse of the function.

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4.3 Use Inverse Functions Pg. 129, 4.3 #1-21

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