1. Warm Up 8/17/17 Find the equation of the line with
Slope:5 and Point: 3,6

2. Inverse Functions

3. Inverse: The opposite. The inverse undoes what the original function does
Here are some “opposites:” −
× ÷
𝑥 𝑥
4, ,4
𝑓(𝑥)
𝑓 −1 (𝑥)

4. 𝑓(𝑥) denotes the original function
𝑓 −1 (𝑥) denotes the inverse function

5. For example, let’s take a look at the square function: f(x) = x2
In the same way, the inverse of a given function will “undo” what the original function did.
For example, let’s take a look at the square function: f(x) = x2 x
f(x) y
f-1(x) 9 3 3 9 9 3 3 9 9 3 3 9 9 3 3 x2 9 9 3 3 9 9 9 3 3 3 9 9

6. For example, let’s take a look at the square function: f(x) = x2
In the same way, the inverse of a given function will “undo” what the original function did.
For example, let’s take a look at the square function: f(x) = x2 x y
f-1(x)
f(x) 5 25 5 5 25 5 25 5 5 25 25 5 5 x2 5 25 25 5 5 25 25 5 25 5 5 5

7. For example, let’s take a look at the square function: f(x) = x2
In the same way, the inverse of a given function will “undo” what the original function did.
For example, let’s take a look at the square function: f(x) = x2 x
f-1(x)
f(x) y 11
121 11 11
121
121 11 11
121
121 11 11 x2
121
121 11
121 11
121 11
121 11 11
121
121
121
121 11 11

8. Graphically, the x and y values of a point are switched.
The point (4, 7)
has an inverse point of (7, 4)
AND
The point (-5, 3)
has an inverse point of (3, -5)

9. Graphically, the x and y values of a point are switched.
If the function y = g(x) contains the points X 1 2 3 4 y 8 16
then its inverse,
y = g-1(x), contains the points x 1 2 4 8 16 y 3
Where is there a line of reflection?

10. y = f(x)
y = x
The graph of a function and its inverse are mirror images about the line
y = f-1(x)
y = x

11. Find the inverse of a function :
Example 1: y = 6x - 12
Step 1: Switch x and y:
x = 6y - 12
Step 2: Solve for y:

12. Graph Linear Equations (and their inverse)
𝑦=3𝑥−6
3 𝑜𝑟 3 1
Slope:
y-int: −6
Inverse:
𝑥=3𝑦−6
𝑥+6=3𝑦
𝑥 = 3𝑦 3
1 3 𝑥+2=𝑦

13. Find the Inverse A. 𝑦=4𝑥−2 B. 𝑦= 𝑥 5 +8 𝑥= 𝑦 5 +8 𝑥=4𝑦−2 +2 +2 −8 −8
− −8
𝑥+2=4𝑦
𝑥−8= 𝑦 5
𝑥 = 4𝑦 4
5(𝑥−8)= 𝑦 5 ∗5
𝑥 =𝑦
5𝑥−40=𝑦

14. Example 2: Given the function : y = 3x2 + 2 find the inverse:
Step 1: Switch x and y:
x = 3y2 + 2
Step 2: Solve for y:

15. Example 2: Given the function : find the inverse:
Step 1: Switch x and y:
Step 2: Solve for y: