1. 7.5 Inverses of Functions 7.5 Inverses of Functions Objectives: Find the inverse of a relation or function Determine whether the inverse of a function is a function

2. Warm-Up Solve each equation for y. 1) x = -4y 2) x = 2y + 3 3) 4)

3. Inverse of a Relation The domain of the inverse is the range of the original relation. The range of the inverse is the domain of the original relation. The inverse of a relation consisting of the ordered pairs (x, y) is the set of all ordered pairs (y, x).

4. Example 2 Find the inverse of each relation. State whether the relation is a function. State whether the inverse is a function. a) {(1,2), (4,-2), (3,2)} inverse: {(2,1), (-2,4), (2,3)} function not a function b) {(-2,4), (3,-4), (-8,-5)} inverse: {(4,-2), (-4,3), (-5,-8)} function

5. Example 3 Find an equation for the inverse of. interchange x and y solve for y -3 5x - 3 = 2y 22

6. Practice Find an equation for the inverse of y = 4x – 5.

7. Warm-Up Find an equation for the inverse of each function. 1) g(x) = -2x - 7 2) 3)

8. Horizontal-Line Test The inverse of a function is a function if every horizontal line intersects the graph of the given function at no more than one point.

9. Horizontal-Line Test not a functionfunction

10. Composition and Inverses If f and g are functions and, then f and g are inverses of one another.

11. Example 1 Show that f(x) = 4x – 3 and are inverses of each other. Since, the two functions are inverses of each other.

12. Practice Show that f(x) = -5x + 7 and are inverses of each other.