1. Look at your quiz You have 10 minutes to work on your quiz again
Fix any mistakes you want. You are allow to work with your TEAM only.
You still need to show your work in order to receive credit
BOX in your FINAL ANSWER

2. Lesson 2.5 Inversed of Functions

3. Review: Operations of Functions
F(x) = 3x + 2 and g(x) = -2x
g + f
f – g
f∙g
g f
g°g

4. Domain and Range
Domain and Range do have restriction.

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

6. Example 1
Find the inverse of each relation. State whether the relation is a function. State whether the inverse is a function. Remember what makes a function a function.
1) {(2, -3), (3, -4), (4, -2)}
2) {(-1, -6), (0, 2), (1, 2), (3, 6)}
inverse: (-3,2), (-4, 3), (-2, 4); yes, and yes
(-6, -1), (2,0), (2,1) (6, 3); yes, no

7. Example 2
Find an equation for the inverse of g(x)= -2x -7 Step: interchange x and y and then solve for y
Inverse: 𝑔 −1 𝑥 = −1 2 𝑥

8. You Try
Step: interchange x and y and then solve for y Find an equation for the inverse of g x = 𝑥−1 4
Inverse: 𝑔 −1 𝑥 = −1 2 𝑥

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

10. You Try

11. Example 3
Show that f(x) = 7x – 2 and g(x) = 1/7 x +2/7 are in verses of each other. Rule: if f and g are functions and (f°g)(x) = (g°f)(x)=I(x)=x, then f and g are inverse of one another.

12. You Try
For each function, find an equation for the inverse. Then use composition to verify that the equation you wrote is the inverse. f x = 𝑥−3 2

13. Homework
Lesson 2.5 page 122 #12-40 even