1. INVERSE
FUNCTIONS

2. Steps for Finding the Inverse of a Function
y = f -1(x)
Solve for y
Trade x and y places
Replace f(x) with y

3. Let’s check this by doing
Find the inverse of
y = f -1(x)
Solve for y
Trade x and y places
Replace f(x) with y

4. Find the inverse of a function :
Example 1: f(x) = 6x - 12
Step 1: Change f(x) to y:
y = 6x - 12
Step 2: Switch x and y:
x = 6y - 12
Step 3: Solve for y:
x +12 = 6y
𝒙+𝟏𝟐 𝟔 =y
𝒚= 𝒙 𝟔 +2
Step 4: Change y to 𝒇 −𝟏 𝒙 :
𝒇 −𝟏 (x) = 𝒙 𝟔 +2

5. Given the function: f(x) = 3x2 + 2 find the inverse:
Example 2:
Given the function: f(x) = 3x find the inverse:
Step 1: Change f(x) to y:
y = 3x2 + 2
Step 2: Switch x and y:
x = 3y2 + 2
Step 3: Solve for y:
Step 4: Change y to 𝒇 −𝟏 𝒙 :
𝑓 −1 (𝑥)= 𝑥−2 3

6. Ex: Find an inverse of y = -3x+6.
Steps: -switch x & y
-solve for y
y = -3x+6
x = -3y+6
x-6 = -3y

7. Finding the Inverse
Try