Cube & Cube Root Inverses and solving

Cube & Cube Root Inverses and solving

By Chrissy Rogers

Fill in the Blanks

Simplify the Expression

$3^3$  

Fill in the Blanks

Simplify the Expression

$4^3$  

Fill in the Blanks

Simplify the Expression $\left(-1\right)^3$  

Fill in the Blanks

Simplify the Expression

$\left(-2\right)^3$  

Fill in the Blanks

Simplify the Expression $\sqrt[3]{64}$  

Fill in the Blanks

Simplify the Expression

$\sqrt[3]{-1000}$  

Poll

$$\sqrt[3]{2x+1}=-3$$  

What do you get when you cube both sides?

• $$2x+1=-3$$  

• $$2x+1=9$$  

• $$2x+1=-27$$  

• Not Sure

​Solving Cube Root Equation

Review: Finding Algebraic Inverses

Multiple Choice

$$Solve\ \ \ \ \sqrt[3]{x-1}=7$$  

• 344

• 22

• 342

• 20

• 50

Multiple Choice

$$Solve\ \ \ \ \sqrt[3]{x+16}=10$$  

• 1016

• 984

• 14

• 84

• 46

Multiple Choice

$$Solve\ \ \ \ -4\sqrt[3]{x+10}=-40$$  

• 900

• 990

• -110

• 90

• -1010

Multiple Choice

$$Solve\ \ \ \ -11\sqrt[3]{x}+13=-20$$  

• 27

• -27

• 9

• 30

• 8

Multiple Choice

Find the inverse: $$f\left(x\right)=x^3-1$$  

• $$f^{-1}\left(x\right)=\sqrt[3]{3x+1}$$  

• $$f^{-1}\left(x\right)=\sqrt[3]{x-1}$$  

• $$f^{-1}\left(x\right)=\frac{x-1}{3}$$  

• $$f^{-1}\left(x\right)=\frac{x+1}{3}$$  

Multiple Choice

Find the inverse of   $$f\left(x\right)=\sqrt[3]{x+3}$$  

• $$f^{-1}\left(x\right)=x^3-3$$  

• $$f^{-1}\left(x\right)=\left(x-3\right)^3$$  

• $$f^{-1}\left(x\right)=x^3+3$$  

• $$f^{-1}\left(x\right)=\left(x+3\right)^3$$  

Multiple Choice

Find the inverse of $$f\left(x\right)=\left(x+2\right)^3+7$$  

• $$f^{-1}\left(x\right)=\sqrt[3]{x-7}-2$$  

• $$f^{-1}\left(x\right)=\sqrt[3]{x-2}-7$$  

• $$f^{-1}\left(x\right)=\left(x-7\right)^3-2$$  

• $$f^{-1}\left(x\right)=\left(x-2\right)^3-7$$  

Multiple Choice

$$Find\ the\ inverse\ of\ f\left(x\right)=\left(x-5\right)^3-4$$  

• $$f^{-1}\left(x\right)=\sqrt[3]{x+5}+4$$  

• $$f^{-1}\left(x\right)=\sqrt[3]{x+4}+5$$  

• $$f^{-1}\left(x\right)=\sqrt[3]{x-5}-4$$  

• $$f^{-1}\left(x\right)=\sqrt[3]{x-4}-5$$  

Multiple Choice

$$Find\ the\ inverse\ of\ f\left(x\right)=\sqrt[3]{x+8}-6$$  

• $$f^{-1}\left(x\right)=\left(x+6\right)^3-8$$  

• $$f^{-1}\left(x\right)=\left(x-6\right)^3+8$$  

• $$f^{-1}\left(x\right)=\left(x+8\right)^3-6$$  

• $$f^{-1}\left(x\right)=\left(x-8\right)^3+6$$  

Multiple Choice

$$Find\ the\ inverse\ of\ f\left(x\right)=\sqrt[3]{4x}-3$$  

• $$f^{-1}\left(x\right)=4\left(x+3\right)^3$$  

• $$f^{-1}\left(x\right)=\frac{\left(x-3\right)^3}{4}$$  

• $$f^{-1}\left(x\right)=\frac{x^3}{4}+3$$  

• $$f^{-1}\left(x\right)=\frac{\left(x+3\right)^3}{4}$$