1. Finding Inverses of Cubic Functions

2. Essential Question
How can I use solving techniques to find the inverse of a cubic function?

3. Steps Rewrite f(x)= as y= Switch x & y Solve for y
(ISOLATE) Add/subtract the constant
(ISOLATE) Divide by the coefficient of cubed expression
(RECIPROCAL POWER) Take the cube root of both sides
(SOLVE) Add/subtract the constant
(SOLVE) Divide by the coefficient
Rewrite the inverse function as f-1(x)=

4. Example 1: Find the inverse of f(x)=2(x-3)3 + 5
y=2(x-3)3 + 5
Rewrite f(x)= as y=
Switch x & y
Solve for y
Add/subtract the constant
Divide by the coefficient of cubed expression
Take the cube root of both sides
Divide by the coefficient
Rewrite the inverse function as f-1(x)=
x=2(y-3)3 + 5
x-5=2(y-3)3
𝑥−5 2 = (𝑦−3) 3
3 𝑥−5 2 =𝑦−3
3 𝑥− =𝑦
𝑓 −1 (𝑥)= 3 𝑥−
No coefficient

5. Try this one… Find the inverse of 𝑓 𝑥 =− 𝑥−2 3 +9
REWRITE: y = -(x – 2)3 + 9
Switch the x & y: x = -(y – 2)3 + 9
Subtract 9: x – 9 = -(y – 2)3
Divide by -1: – x = (y – 2)3
Take the Cube root: −𝑥 =𝑦 −2
Add 2: −𝑥 +2=𝑦
Rewrite in INVERSE form 𝑓 −1 𝑥 = 3 9−𝑥 +2

6. Try these for HW (Practice)…
Find the inverse of
1. 𝑓 𝑥 =− 𝑥−
2. 𝑓 𝑥 =− 𝑥
3. 𝑓 𝑥 =3 𝑥 3 −1
4. 𝑓 𝑥 =2 𝑥+4 3 −7