Question

The transformation of 'f' is represented by 'g'. Write a rule for g. f(x)=\root(3)(x). Then show your check steps.

Answer 1

`g(x)=-2\sqrt[3]x`

or

`g(x) = -2f(x)`

Explanation:

Given

`f(x) = \sqrt[3]x`

Required

Write a rule for g(x)

See attachment for grid

From the attachment, we have:

`(x_1,y_1) = (-1,2)`

`(x_2,y_2) = (1,-2)`

We can represent g(x) as:

`g(x) = n * f(x)`

So, we have:

`g(x) = n * \sqrt[3]x`

For:

`(x_1,y_1) = (-1,2)`

`2 = n * \sqrt[3]{-1}`

This gives:

`2 = n * -1`

Solve for n

`n = (2)/(-1)`

`n = -2`

To confirm this value of n, we make use of:

`(x_2,y_2) = (1,-2)`

So, we have:

`-2 = n * \sqrt[3]1`

This gives:

`-2 = n * 1`

Solve for n

`n = (-2)/(1)`

`n = -2`

Hence:

`g(x) = n * \sqrt[3]x`

`g(x)=-2\sqrt[3]x`

or:

`g(x) = -2f(x)`