Question

combining functionsconsider the following functions find the formula for (f/g)(x) and simplify your answer

Answer 1

Given the functions

`f(x)=\sqrt[]{(x-4)}`
`g(x)=x^{(2)/(3)}`

You have to calculate

`((f)/(g))(x)`

This is a division between both functions. FIrstI'm going to rewrite the exponent for the first function:

`\begin{gathered} f(x)=\sqrt[]{(x-4)} \\ f(x)=\sqrt[]{x}-\sqrt[]{4} \\ f(x)=x^{(1)/(2)}-2 \end{gathered}`

Now proceed solving the division

`\begin{gathered} ((f)/(g))(x) \\ \frac{x^{(1)/(2)}-2}{x^{(2)/(3)}}=\frac{x^{(1)/(2)}}{x^{(2)/(3)}}-\frac{2}{x^{(2)/(3)}} \\ x^{((1)/(2)-(2)/(3))}-\frac{2}{x^{(2)/(3)}} \\ x^{-(1)/(6)}-\frac{2}{x^{(2)/(3)}} \\ \frac{1}{\sqrt[6]{x}}-\frac{2}{x^{(2)/(3)}} \end{gathered}`