Determine the function for (f/g)(x).
[tex]\begin{gathered} (\frac{f}{g})(x)=\frac{f(x)}{g(x)} \\ =\frac{\sqrt[3]{4x}}{2x+3} \end{gathered}[/tex]
For the function (f/g)(x) to be defined the denominator must not equal to 0. So,
[tex]\begin{gathered} 2x+3\ne0 \\ 2x\ne-3 \\ x\ne-\frac{3}{2} \end{gathered}[/tex]
Thus answer is,
[tex](\frac{f}{g})(x)=\frac{\sqrt[3]{4x}}{2x+3},x\ne-\frac{3}{2}[/tex]
Option D is correct.
