Given:
[tex]\begin{gathered} f(x)=\text{ }\frac{1}{x} \\ g(x)=x^3 \end{gathered}[/tex]Required:
[tex](\frac{f}{g})(x)[/tex]Re-writing the given expression:
[tex](\frac{f}{g})(x)\text{ = }\frac{f(x)}{g(x)}[/tex]Hence:
[tex]\begin{gathered} \frac{f(x)}{g(x)}=\text{ }\frac{\frac{1}{x}}{x^3} \\ =\text{ }\frac{1}{x}\times\frac{1}{x^3} \\ =\text{ }\frac{1}{x^4} \end{gathered}[/tex]Answer:
[tex](\frac{f}{g})(x)=\frac{1}{x^4}[/tex]