Question

Find f/g for the functions provided. 10 points Help needed.

Answer 1

ANSWER

$( \frac{f}{g} )(x) = \frac{1}{3} ( {x}^{2} + 3x + 9)$

EXPLANATION

The given functions are

$f(x) = {x}^{3} - 27$

and

$g(x) = 3x - 9$

$( \frac{f}{g} )(x) = \frac{f(x)}{g(x)}$

$( \frac{f}{g} )(x) = \frac{ {x}^{3} - 27}{3x - 9}$

$( \frac{f}{g} )(x) = \frac{ (x - 3)( {x}^{2} + 3x + 9) }{3(x -3 )}$

Cancel the common factors,

$( \frac{f}{g} )(x) = \frac{ {x}^{2} + 3x + 9 }{3}$

OR

$( \frac{f}{g} )(x) = \frac{1}{3} ( {x}^{2} + 3x + 9)$