How do I find the inverse of functions?

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.”

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

4.3 Use Inverse Functions Example 1 Verify that functions are inverses

4.3 Use Inverse Functions Example 1 Verify that functions are inverses

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

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.

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) = _____.

4.3 Use Inverse Functions Checkpoint. Complete the following exercise.

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.

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 ) = ______. )

4.3 Use Inverse Functions Checkpoint. Complete the following exercise.

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

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

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