1. Section 4.7 Day 1 Inverse Linear Functions
Algebra 1

2. Learning Targets
Define & recognize an inverse relation from a graph & table
Determine the inverse of a relation from a table, ordered pairs, and a graph
Construct the inverse of a function from an equation
Use inverse relationships to solve a problem in a context

3. Ingredients for a cookie Ingredients for a cookie
Inverse Relation X Y
Ingredients for a cookie
Ex: flour, sugar, chocolate chips, etc.
Final cookie
Ex: Chocolate Chip Cookie Y x
Final cookie
Ex: Chocolate Chip Cookie
Ingredients for a cookie
Ex: flour, sugar, chocolate chips, etc.
Process of Inverse Function

4. Deconstructing and reversing a relation We denote it by 𝑓 −1 (𝑥)
Inverse Relation
Deconstructing and reversing a relation We denote it by 𝑓 −1 (𝑥)

5. Example 1 What is the inverse of the relation? X -4 -1 5 9 Y -13 -8.5
0.5
6.5 X
-13
-8.5
0.5
6.5 Y -4 -1 5 9

6. Example 2
What is the inverse of the relation? { 4, −10 , 7,−19 , −5, 17 , −3, 11 } { −10, 4 , −19, 7 , 17, −5 , 11, −3 }

7. Example 3
Find the inverse of 𝑓 𝑥 =4𝑥−8 1. Replace 𝑓(𝑥) with 𝑦: 𝑦=4𝑥−8 2. Switch 𝑥 & 𝑦: 𝑥=4𝑦−8 3. Solve for y: 𝑥+8=4𝑦 𝑥+8 4 =𝑦 4. The inverse is 𝑓 −1 𝑥 = 𝑥+8 4

8. Example 4
Find the inverse of 𝑓 𝑥 =10𝑥−9 1. Replace 𝑓(𝑥) with 𝑦: 𝑦=10𝑥−9 2. Switch 𝑥 & 𝑦: 𝑥=10𝑦−9 3. Solve for y: 𝑥+9=10𝑦 𝑥+9 10 =𝑦 4. The inverse is 𝑓 −1 𝑥 = 𝑥+9 10

9. Example 5
Find the inverse of 𝑓 𝑥 =− 1 2 𝑥 Replace with 𝑦: 𝑦=− 1 2 𝑥 Switch: 𝑥=− 1 2 𝑦 Solve: 𝑥−11=− 1 2 𝑦 −2 𝑥−11 =−2𝑥+22=𝑦 4. Inverse: 𝑓 −1 𝑥 =−2𝑥+22

10. Example 6
The following table represents the function 𝑓(𝑥). What is the value of 𝑓 −1 (4)?
𝑓 −1 (4) is looking for where does 𝑓(𝑥) have 4 as the y- value.
This is when 𝑥=2. Thus 𝑓 −1 4 =2 x
f(x) -4 2 4 5
-10 9

11. Example 7
The following table represents the function 𝑓(𝑥). What is the value of 𝑓 −1 (10)?
𝑓 −1 (4) is looking for where does 𝑓(𝑥) have 10 as the y- value.
This is when 𝑥=9. Thus 𝑓 −1 4 =9 x
f(x) -3 2 14 10 -1 9

12. Homework
Pg : #16, 17, 18, 38