1. SAT Problem of the Day

2. 2.5 Inverses of Functions 2.5 Inverses of Functions Objectives: Find the inverse of a relation or function Determine whether the inverse of a function is a function

3. Example 1 Solve the equation v = 50 + 3t for t. v = 50 + 3t -50 v - 50 = 3t 33

4. 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).

5. 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

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

7. Practice Find an equation for the inverse of f(x) = 4x – 5.

8. Activity 1)Graph y = 2x – 1. 2) Graph y = x. 3) Graph the inverse of y = 2x – 1. 4) Graph y = -2x + 5 5) Graph y = x. 6) Graph the inverse of y = -2x + 5.

9. Graphs of Inverse Functions The graph of the inverse of a function is the reflection of the graph of the function across the line y = x. Horizontal-Line Test The inverse of a function is a function iff every horizontal line intersects the graph of the given function at no more than one point.

10. Horizontal-Line Test not a functionfunction

11. Composition and Inverses If f and g are functions and (f ○ g)(x) = (g ○ f)(x) = x then f and g are inverses of one another.

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

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

14. Homework More Problems on Inverses

15. Collins Writing Type 1 Compare and contrast the vertical- and horizontal-line tests.