Answer:
[tex]g(x)=-2\sqrt[3]x[/tex]
or
[tex]g(x) = -2f(x)[/tex]
Step-by-step explanation:
Given
[tex]f(x) = \sqrt[3]x[/tex]
Required
Write a rule for g(x)
See attachment for grid
From the attachment, we have:
[tex](x_1,y_1) = (-1,2)[/tex]
[tex](x_2,y_2) = (1,-2)[/tex]
We can represent g(x) as:
[tex]g(x) = n * f(x)[/tex]
So, we have:
[tex]g(x) = n * \sqrt[3]x[/tex]
For:
[tex](x_1,y_1) = (-1,2)[/tex]
[tex]2 = n * \sqrt[3]{-1}[/tex]
This gives:
[tex]2 = n * -1[/tex]
Solve for n
[tex]n = \frac{2}{-1}[/tex]
[tex]n = -2[/tex]
To confirm this value of n, we make use of:
[tex](x_2,y_2) = (1,-2)[/tex]
So, we have:
[tex]-2 = n * \sqrt[3]1[/tex]
This gives:
[tex]-2 = n * 1[/tex]
Solve for n
[tex]n = \frac{-2}{1}[/tex]
[tex]n = -2[/tex]
Hence:
[tex]g(x) = n * \sqrt[3]x[/tex]
[tex]g(x)=-2\sqrt[3]x[/tex]
or:
[tex]g(x) = -2f(x)[/tex]
