Question

For the functions f(x)=x/x-3 and g(x)=13/xFind the composition f • x and simplify your answer as much as possible.Write the domain using interval (F•g)(x)=Domain of f•g:

Answer 1

Problem statement

`\begin{gathered} f(x)=\frac{x}{x-3\text{ }} \\ \text{and } \\ g(x)=(13)/(x) \end{gathered}`

Part A

Solution

`(f.g)(x)=((13)/(x))/((13)/(x)-3)`

We can now simplify

`\begin{gathered} (f.g)(x)=((13)/(x))/((13)/(x)-(3)/(1)) \\ \\ (f.g)(x)=((13)/(x))/((13-3x)/(x)) \\ \text{simplifying} \\ (f.g)(x)=(13)/(x)*(x)/(13-3x) \end{gathered}`

`\begin{gathered} (f.g)(x)=(13)/(x)*(x)/(13-3x) \\ x\text{ can divide x we have} \\ \\ (f.g)(x)=(13)/(13-3x) \end{gathered}`

Part B

The Domain

`\begin{gathered} \text{Let set 13-3x=0} \\ 13=3x \\ x=(13)/(3) \end{gathered}`

The domain is

`(-\infty,(13)/(3))\text{ U (}(13)/(3),\infty)`