Given the functions
[tex]f(x)=\sqrt[]{(x-4)}[/tex][tex]g(x)=x^{\frac{2}{3}}[/tex]
You have to calculate
[tex](\frac{f}{g})(x)[/tex]
This is a division between both functions. FIrstI'm going to rewrite the exponent for the first function:
[tex]\begin{gathered} f(x)=\sqrt[]{(x-4)} \\ f(x)=\sqrt[]{x}-\sqrt[]{4} \\ f(x)=x^{\frac{1}{2}}-2 \end{gathered}[/tex]
Now proceed solving the division
[tex]\begin{gathered} (\frac{f}{g})(x) \\ \frac{x^{\frac{1}{2}}-2}{x^{\frac{2}{3}}}=\frac{x^{\frac{1}{2}}}{x^{\frac{2}{3}}}-\frac{2}{x^{\frac{2}{3}}} \\ x^{(\frac{1}{2}-\frac{2}{3})}-\frac{2}{x^{\frac{2}{3}}} \\ x^{-\frac{1}{6}}-\frac{2}{x^{\frac{2}{3}}} \\ \frac{1}{\sqrt[6]{x}}-\frac{2}{x^{\frac{2}{3}}} \end{gathered}[/tex]
