Determine the function (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 real value of the function (f/g)(x), 2x + 3 should not equal to 0. So,
[tex]\text{ 2x + 3 }\ne0[/tex]
Simplify
[tex]2x+3\ne0[/tex]
to obtain the value of x.
[tex]\begin{gathered} 2x+3\ne0 \\ 2x\ne-3 \\ x\ne-\frac{3}{2} \end{gathered}[/tex]
So x should not equal to -3/2. Thus restiction on the function is,
[tex]x\ne-\frac{3}{2}[/tex]
Answer: Option B.
