Question

Help!

Let f(x) = 5x3 − x2 − 60x + 12 and g(x) = 5x − 1. Find f of x over g of x.

A. 2 − 12
B. 5x2 + 4x
C. x2 − 12x
D. 5x2 + 4

Answer 1

x2 − 12 a is correct

Explanation:

Answer 2

Given that the two functions are
`f(x)=5x^3-x^2-60x+12` and
`g(x)=5x-1`

We need to determine the value of
`(f(x))/(g(x))`

The value of
`(f(x))/(g(x))`:

To determine the value of
`(f(x))/(g(x))`, let us substitute the functions
`f(x)=5x^3-x^2-60x+12` and
`g(x)=5x-1` in
`(f(x))/(g(x))`

Thus, we get;

`(f(x))/(g(x))=(5x^3-x^2-60x+12)/(5x-1)`

Let us group the terms in the numerator.

Thus, we get;

`(f(x))/(g(x))=((5x^3-x^2)-(60x-12))/(5x-1)`

Factoring out the common terms from each group, we get;

`(f(x))/(g(x))=(x^2(5x-1)-12(5x-1))/(5x-1)`

Factoring out the term (5x - 1), we have;

`(f(x))/(g(x))=((x^2-12)(5x-1))/(5x-1)`

Cancelling the common terms, we get;

`(f(x))/(g(x))=x^2-12`

Thus, the value of
`(f(x))/(g(x))` is
`x^2-12`

Hence, Option A is the correct answer.