Given:
The functions are:
[tex]f(x)=-4x^2-6x-1[/tex]
[tex]g(x)=-x^2-5x+3[/tex]
To find:
The function [tex](f-g)(x)[/tex].
Solution:
We have,
[tex]f(x)=-4x^2-6x-1[/tex]
[tex]g(x)=-x^2-5x+3[/tex]
We know that,
[tex](f-g)(x)=f(x)-g(x)[/tex]
[tex](f-g)(x)=(-4x^2-6x-1)-(-x^2-5x+3)[/tex]
[tex](f-g)(x)=-4x^2-6x-1+x^2+5x-3[/tex]
Combining like terms, we get
[tex](f-g)(x)=(-4x^2+x^2)+(-6x+5x)+(-1-3)[/tex]
[tex](f-g)(x)=-3x^2+(-x)+(-4)[/tex]
[tex](f-g)(x)=-3x^2-x-4[/tex]
Therefore, the required function is [tex](f-g)(x)=-3x^2-x-4[/tex].
