Question

If f(x) = -x2 + 6x- 1 and g(x) = 3x2- 4x-1, find (f - g)(x).

Answer 1

ANSWER: (f-g) (x)= -4x2+10x

Answer 2

`(f-g)(x)=-4x^2+10x`

Explanation:

We are given the two functions:

`f(x)=-x^2+6x-1\text{ and } g(x)=3x^2-4x-1`

And we want to find:

`(f-g)(x)`

This is equivalent to:

`=f(x)-g(x)`

Substitute:

`=(-x^2+6x-1)-(3x^2-4x-1)`

Distribute:

`=-x^2+6x-1+(-3x^2+4x+1)`

Rearrange:

`=(-x^2-3x^2)+(6x+4x)+(-1+1)`

Combine like terms. Hence:

`(f-g)(x)=-4x^2+10x`