Given: The functions below
[tex]\begin{gathered} f(x)=-x^2 \\ g(x)=-(x+4)^2 \end{gathered}[/tex]To Determine:
[tex](f-g)(x)[/tex]Solution
[tex](f-g)(x)=f(x)-g(x)[/tex][tex]\begin{gathered} =-x^2-(-(x+4)^2) \\ =-x^2+(x+4)^2 \\ =-x^2-(x^2+8x+16) \\ =-x^2-x^2-8x-16 \\ =-2x^2-8x-16 \end{gathered}[/tex]Hence
[tex](f-g)(x)=-2x^2-8x-16[/tex]