Question

If f(x)=x^2+3xAnd g(x)=4-xWhat is (f/g)(x)= (f/g)(5)=

Answer 1

Given: A function

`f(x)=x^2+3x`

and

`g(x)=4-x`

Required: To find the function-

`((f)/(g))(x)\text{ and }((f)/(g))(5)`

Step-by-step explanation: The required function can be calculated as

`\begin{gathered} ((f)/(g))(x)=(f(x))/(g(x)) \\ =(x^2+3x)/(4-x) \\ =(x(x+3))/(4-x) \end{gathered}`

Now putting x=5 gives-

`\begin{gathered} ((f)/(g))(5)=(5^2+3(5))/(4-5) \\ =(25+15)/(-1) \\ =-40 \end{gathered}`

Final Answer: The required function is

`((f)/(g))(x)=(x(x+3))/(4-x)`

and

`((f)/(g))(5)=-40`