1. 7-8: Inverse Functions and Relations

2. Terms to Know Inverse relation: the set of ordered pairs obtained by reversing the coordinates of each original ordered pairs. Inverse function: two functions f and g are inverse functions if and only if both of their compositions are the identity function

3. Key Concept Words: Two examples are inverse relations if and only if whenever one relation contains the element (a,b), the other relation contains the element (b,a) Example: Q = {(1,2), (3,4), (5,6)} S = {(2,1), (4,3), (6,5)} S = {(2,1), (4,3), (6,5)} Q and S are inverse relations

4. Property of Inverse Function Suppose and are inverse functions. Then, if and only if if and only if

5. Some Practice Problems Step 1: Replace f(x) with y in the original equation Step 2: Interchange x and y Step 3: Solve for y Inverse Multiply each side by 2 Find the inverse of Next slide

6. Subtract 6 from each side Step 4: Replace y with f (x) f (x) = 2x - 6 The inverse of f(x) = is f (x) = 2x - 6 x+6 2

7. More Practice Problems Determine whether f(x) = 5x + 10 and g(x) = x – 2 are inverse functions 5 1 Check to see if the compositions of f(x) and g(x) are identity functions. [f g](x) = f[g(x)] = f( x -2) 1 5 = = = The functions are inverses since both [f g](x) and [g f](x) equal x