1. 7.8 Inverse Functions and Relations Horizontal line Test

2. Look at the functions f(x) and g(x) f(x) = 2x + 4g(x) = ½x – 2 (x, f(x))(x,g(x)) (-1,2)(2,-1) (0,4)(4,0) (1,6)(6,1) (2,8)(8,2) What do you see?

3. Look at the functions f(x) and g(x) f(x) = 2x + 4g(x) = ½x – 2 (x, f(x))(x, g(x)) (-1,2)(2,-1) (0,4)(4,0) (1,6)(6,1) (2,8)(8,2) The two functions are inverses of each other

4. Definition of Inverse Functions A function and its inverse function can be described as the "DO" and the "UNDO" functions. A function takes a starting value, performs some operation on this value, and creates an output answer. The inverse function takes the output answer, performs some operation on it, and arrives back at the original function's starting value. http://www.regentsprep.org/Regents/math/algtrig/ATP8/inverselesson.htm

5. How to find an inverse function Since the input and output switch places. x and y will switch places. FunctionInverse y = 4x +12x = 4y + 12 4y = x- 12 y = ¼x – 3

6. Find the inverse of y = 5x - 20 Switch x and y

7. Find the inverse of y = 5x - 20 Switch x and y

8. Find the inverse of y = 5x - 20 Switch x and y

9. Graph the function and it inverse

10. The graphs the function and its inverse reflect over a line y=x

11. To check if two functions are inverse we use compositions Let If both compositions equal x, then the functions are inverses

12. To check if two functions are inverse we use compositions If both compositions equal x, then the functions are inverses

13. Inverses can be written as If both compositions equal x, then the functions are inverses

14. Horizontal Line test If a Horizontal line can pass through a graph of a function only touching it at one point, then the graph has a inverse. YesNo

15. Homework Page 393 – # 15, 21, 24, 27, 30, 33, 36

16. Homework Page 393 – # 18, 20, 23, 26, 29, 32, 35