Question

Find (f/g) (x) for the functions provided: ƒ(x) = x3 − 27, g(x) = 3x − 9

Answer 1

Explanation:

Answer 2

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

Explanation:

We have been given that

`f(x)=x^3-27,g(x)=3x-9`

We can use the formula for difference of cubes to simplify the function f(x)

difference of cubes -
`a^3-b^3=(a-b)(a^2+ab+b^2)`

`f(x)=x^3-27\\\\=x^3-3^3\\\\=(x-3)(x^2+3x+9)`

And g(x) can be written as

`g(x)=3x-9\\=3(x-3)`

Thus, we have

`((f)/(g))(x)=((x-3)(x^2+3x+9))/(3(x-3)`

On cancelling the common factors, we get

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