Inverses of Cubes and Cube Roots

We will derive the inverse of a cubic and cube root function.
I will summarize the process to derive the inverses of cubic and cube root functions.
TEK 2A.2B&2C

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Lesson 4 Writing the inverse of Cubic and Cube root Functions

Dropdown

a=​ ​

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b=​

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c=​

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d=​

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According to the a value, the graph reflects across the ​

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Inverses graphs reflect over the y=x line...why?

Due to the fact their x and y values switch!

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Review of inverses...

Reorder

Reorder the following steps, they have been simplified...

• Change f(x) to y

• Switch x and y

• Solve for y

• Change y to f(x)

1

2

3

4

• 1
• 2
• 3
• 4

Multiple Choice

The correct inverse for example A is?

• $$y=\ \sqrt[3]{x-1}$$

• $$y=\sqrt[3]{x}-1$$

• $$y=\sqrt[3]{x+1}$$

• $$y=\sqrt[3]{x}+1$$

Multiple Choice

The correct inverse for example B is?

• $$f^{-1}\left(x\right)=\sqrt[3]{x-2}-5$$

• $$f^{-1}\left(x\right)=\sqrt[3]{x-5}-2$$

• $$f^{-1}\left(x\right)=\sqrt[3]{x+2}-5$$

• $$f^{-1}\left(x\right)=\sqrt[3]{x+5}-2$$

Multiple Choice

The correct inverse for Example C is?

• $$y=\left(x-3\right)^3+7$$

• $$y=\left(x-7\right)^3+3$$

• $$y=\left(x+3\right)^3+7$$

• $$y=\left(x+7\right)^3+3$$

Multiple Choice

The correct inverse for example D is?

• $$f^{-1}\left(x\right)=\frac{\left(x^3-5\right)}{3}$$

• $$f^{-1}\left(x\right)=\frac{\left(x-5\right)^3}{3}$$

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

• $$f^{-1}\left(x\right)=\frac{x^3}{3}-5$$

Multiple Choice

The correct inverse for example E is?

• $$y=\left(5\left(x+2\right)\right)^3$$

• $$y=\sqrt[3]{5\left(x+2\right)}$$

• $$y=\left(2\left(x+5\right)\right)^3$$

• $$y=\sqrt[3]{2\left(x+5\right)}$$

Poll

On a scale of 1-5, how confident are you in finding inverses of cubic and cube root functions?

• 5 - I totally understand how to find inverses no problem!

• 4 - I feel pretty good about finding inverses.

• 3 - Maybe some more practice and I'll get it better.

• 2 - I am struggling with a few things and need some clarification

• 1 - I am completely lost..... help...