Question

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

Answer 1

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

Explanation:

The given functions are

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

and

`g(x)=3x-9`

We want to find
`((f)/(g))(x)` of the given functions.

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

`\Rightarrow ((f)/(g))(x)=(x^3-27)/(3x-9)`

`\Rightarrow ((f)/(g))(x)=(x^3-3^3)/(3x-9)`

Recall that;

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

We apply this property to factor the numerator to obtain;

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

We cancel out the common factors to obtain;

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