Question

Given that f(x) = x^2 - 8x + 12 and g(x) = -6, find (f/g)(x) and express the result in standard form

Answer 1

We are given the following two functions

$\begin{gathered} f(x)=x^2-8x+12 \\ g(x)=-6_{} \end{gathered}$

We are to find (f/g)(x)

(f/g)(x) is basically the division of function f(x) by function g(x)

$(\frac{f}{g})(x)=\frac{f(x)}{g(x)}=\frac{x^2-8x+12}{-6}=\frac{x^2}{-6}-\frac{8x}{-6}+\frac{12}{-6}=-\frac{1}{6}x^2+\frac{2}{3}x-2$

Therefore, the function (f/g)(x) is

$(\frac{f}{g})(x)=-\frac{1}{6}x^2+\frac{2}{3}x-2$