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

Question

asked Sep 18, 2023 94.4k views

1 Answer

Jmoerdyk · Answer 1 · 2023-09-22T01:46:59+0000

Given the function f(x):

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

And the function g(x):

You can find

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:

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.