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-

$(\frac{f}{g})(x)\text{ and }(\frac{f}{g})(5)$

Explanation: The required function can be calculated as

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

Now putting x=5 gives-

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

Final Answer: The required function is

$(\frac{f}{g})(x)=\frac{x(x+3)}{4-x}$

and

$(\frac{f}{g})(5)=-40$