Question

If f(x)=-4^2-6x-1 and g(x)=-x^2-5x+3 find (f-g)(x)

Answer 1

Given:

The functions are:

`f(x)=-4x^2-6x-1`

`g(x)=-x^2-5x+3`

To find:

The function
`(f-g)(x)`.

Solution:

We have,

`f(x)=-4x^2-6x-1`

`g(x)=-x^2-5x+3`

We know that,

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

`(f-g)(x)=(-4x^2-6x-1)-(-x^2-5x+3)`

`(f-g)(x)=-4x^2-6x-1+x^2+5x-3`

Combining like terms, we get

`(f-g)(x)=(-4x^2+x^2)+(-6x+5x)+(-1-3)`

`(f-g)(x)=-3x^2+(-x)+(-4)`

`(f-g)(x)=-3x^2-x-4`

Therefore, the required function is
`(f-g)(x)=-3x^2-x-4`.