Question

F(x) =3^√ 3x g(x) = 3x +2 Find (f/g) (x). Include any restrictions on the domain .

Answer 1

Given the function f(x):

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

And the function g(x):

`g(x)=3x+2`

You can find

`((f)/(g))(x)`

by dividing the function f(x) by the function g(x).

Then you can set up the following:

`((f)/(g))(x)=\frac{\sqrt[3]{3x}}{3x+2}`

Now, to find the restrictions, you need to remember that the denominator can't be zero. Then, you can set up this equation:

`3x+2=0`

Solve for "x":

`\begin{gathered} 3x=0-2 \\ 3x=-2 \\ \\ x=-(2)/(3) \end{gathered}`

Therefore, you can conclude that:

`x\\e-(2)/(3)`

Based on the above, you know that the answer is: Option A.