Question

Suppose that the functions f and f are defined as follows F(x)= 5/x g(x)=9/x+1 Find g/f then give its domain using an interval or union of intervals Simplify your answers (g/f)(x)=Domain of g/f:

Answer 1

Given:

`\begin{gathered} f(x)=(5)/(x) \\ g(x)=(9)/(x+1) \end{gathered}`

To find

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

We know that,

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

So,

`\begin{gathered} ((g)/(f))(x)=((9)/(x+1))/((5)/(x)) \\ ((g)/(f))(x)=(9)/(x+1)*(x)/(5) \\ ((g)/(f))(x)=(9x)/(5(x+1)) \end{gathered}`

Hence, the answer is,

`((g)/(f))(x)=(9x)/(5(x+1))`

Domain of the above function is,

Let the dinominator equals to 0, we get

x+1=0

x= -1

Hence, the domain of the function is,

`(-\infty,-1)\cup(-1,\infty)`