Answer:
[tex](\frac{f}{g})(x)\text{ = }\frac{\sqrt[3]{3x}}{3x+2},\text{ x}\ne\text{ -}\frac{2}{3}[/tex]
Explanation:
Here, we want to evaluate the function division
Mathematically, we have this as follows:
[tex](\frac{f}{g})(x)\text{ = }\frac{f(x)}{g(x)}\text{ = }\frac{\sqrt[3]{3x}}{3x+2}[/tex]
Finally, we need to get the domain restriction
To get the domain restriction, we need to find the value of x under which the denominator becomes zero
Mathematically, we have this as:
[tex]\begin{gathered} 3x\text{ + 2= 0} \\ 3x\text{ = -2} \\ x\text{ = -}\frac{2}{3} \end{gathered}[/tex]
Thus, we have the correct representation as:
[tex](\frac{f}{g})(x)\text{ = }\frac{\sqrt[3]{3x}}{3x+2},\text{ x}\ne\text{ -}\frac{2}{3}[/tex]
