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

Answer:

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

or

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

Step-by-step 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

$n = \frac{2}{-1}$

$n = -2$

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

$n = \frac{-2}{1}$

$n = -2$

Hence:

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

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

or:

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