Cube Root Functions

Cube Root Functions

Where does a cube root function come from?

Look at the cubic function to the right. To find the inverse, switch the x column with the y column.

Good news!

We don't have to worry about restricting any domain here because when we switch our x and y columns, we still have a function! The domain and range of both a cubic function and a cube root function are all real numbers. 

Example 1: Find the inverse of the table and graph the function.

Example 2: Find the inverse of the table and graph the function

Multiple Select

Check all of the ordered pairs that are on the inverse of f(x).

• (-3, -1)

• (0, 1)

• (15, 2)

• (1, 1)

• (2, 17)

Multiple Select

Check all of the ordered pairs that are on the inverse of f(x).

• (0, -1)

• (0, 1)

• (16, -3)

• (2, 2)

• (-1, 16)

How do we find the inverse of a cubic function algebraically?

Same as any function- switch x and y and solve for y.

When you find an inverse, remember to use inverse operations starting on the outside.

Multiple Choice

What is the next step in finding the inverse?

• switch x and y

• add 3 to both sides

• subtract 3 from both sides

• divide by 5

Multiple Choice

What is the next step in finding the inverse?

• switch x and y

• take the cube root of both sides

• add 4 to both sides

• divide by 3