Given the function f(x):
[tex]f(x)=\sqrt[3]{3x}[/tex]
And the function g(x):
[tex]g(x)=3x+2[/tex]
You can find
[tex](\frac{f}{g})(x)[/tex]
by dividing the function f(x) by the function g(x).
Then you can set up the following:
[tex](\frac{f}{g})(x)=\frac{\sqrt[3]{3x}}{3x+2}[/tex]
Now, to find the restrictions, you need to remember that the denominator can't be zero. Then, you can set up this equation:
[tex]3x+2=0[/tex]
Solve for "x":
[tex]\begin{gathered} 3x=0-2 \\ 3x=-2 \\ \\ x=-\frac{2}{3} \end{gathered}[/tex]
Therefore, you can conclude that:
[tex]x\ne-\frac{2}{3}[/tex]
Based on the above, you know that the answer is: Option A.
