Question

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

Answer 1

`( (f)/(g) )(x) = (1)/(3) ( {x}^(2) + 3x + 9)`

Step-by-step explanation

The given functions are

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

and

`g(x) = 3x - 9`

`( (f)/(g) )(x) = (f(x))/(g(x))`

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

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

Cancel the common factors,

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

OR

`( (f)/(g) )(x) = (1)/(3) ( {x}^(2) + 3x + 9)`