The document contains notes from a math class on finding the inverse of a relation. It includes examples of finding the inverse of various functions by switching the x and y values. It also provides practice problems for students to find the inverse of given functions and to evaluate composite functions at given values.

1. MB43 9/8/08 Lomas Aim: How do we find the inverse of a relation? Do Now: HW Review: pg 546 # 2,11, 27, 51 f(x) = 2x g(x) = 3x - 5 a) find (f g)(4) b) find the rule for (f g)(x) c) find (f g)(4) using the rule you found in part b HW: Read 548-552 Do 552-3 #1-3,5-10,18-21

2. MB43 9/8/08 Lomas Aim: How do we find the inverse of a relation? What is the identity element under addition? What is the identity element under multiplication? What is the inverse property under addition? What is the inverse property under multiplication? HW: Read 548-552 Do 552-3 #1-3,5-10,18-21

3. MB43 9/8/08 Lomas Aim: How do we find the inverse of a relation? 5 7 9 2 3 4 Is this a function? Why? 5 7 9 2 3 4 This is it's inverse Is this a function? Why? HW: Read 548-552 Do 552-3 #1-3,5-10,18-21

4. MB43 9/8/08 Lomas Aim: How do we find the inverse of a relation? You can find a relation's inverse by switching all the x's for the y's and vice-versa f = { (3,-1), (4,2), (9,-7) } Find the inverse f -1 HW: Read 548-552 Do 552-3 #1-3,5-10,18-21

5. MB43 9/8/08 Lomas Aim: How do we find the inverse of a relation? Try to find a function whose inverse is NOT a function HW: Read 548-552 Do 552-3 #1-3,5-10,18-21

6. MB43 9/8/08 Lomas Aim: How do we find the inverse of a relation? Write the equation of the inverse function: y = 2x + 3 HW: Read 548-552 Do 552-3 #1-3,5-10,18-21

7. MB43 9/8/08 Lomas Aim: How do we find the inverse of a relation? Practice: Find the inverse 1) f(x) = {(0,-4), (1,-3), (2,-1), (3,0), (4,2), (5,3)} 2) f(x) = x + 1 3) f(x) = 2x -3 4) f(x) = 2x + 1 5) f(x) = {(0,0), (1,2), (2,3), (3,4), (4,6), (5,8)} 6) f(x) = {(0,0), (1,1), (2,2), (3,4), (4,6), (5,8)} Find f(g(x)) or g(f(x)) as noted: 7) f(x)= x -4 g(x)= -2x 2 + 4x Find g(f(x)) Evaluate: 9) Find f(-1) when f(x)=4x 8) f(x)=3x + 5 g(x)=2x + 2 Find (g o f)(x) 10) Find f(-4) when f(x) = 3x 2 + x + 2 HW: Read 548-552 Do 552-3 #1-3,5-10,18-21