Question

suppose that the functions f and g are defined as follows. find F/g.then, give its domain using an interval or Union of intervals. simplify your answers.

Answer 1

f/g can be determined as,

`\begin{gathered} (f)/(g)=((9)/(x+5))/((4)/(x)) \\ =(9x)/(4(x+5)) \end{gathered}`

Domain of f(x) is,

`\begin{gathered} x+5\\e0 \\ x\\e-5 \end{gathered}`

Domain of g(x) is,

`x\\e0`

Thus, the domain of f/g is,

`\begin{gathered} x\\e0\text{ and x}\\e-5 \\ x\in R-\lbrace-5,0\rbrace \end{gathered}`

Thus, above expression gives the required domain of f/g.