Question

Find the indicated function and state the domain, in interval notation, of each resulting function.Question 15

Answer 1

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

For the given functions:

`\begin{gathered} f(x)=x-3 \\ g(x)=\sqrt[]{x-3} \end{gathered}`
`\begin{gathered} ((f)/(g))(x)=\frac{x-3}{\sqrt[]{x-3}} \\ \\ \text{Simplify:} \\ ((f)/(g))(x)=\frac{x-3}{\sqrt[]{x-3}}\cdot\frac{\sqrt[]{x-3}}{\sqrt[]{x-3}} \\ \\ ((f)/(g))(x)=\frac{x-3\cdot\sqrt[]{x-3}}{(\sqrt[]{x-3})^2} \\ \\ ((f)/(g))(x)=\frac{x-3\cdot\sqrt[]{x-3}}{x-3^{}} \\ \\ ((f)/(g))(x)=\sqrt[]{x-3} \end{gathered}`