By definition you know that
[tex](f+g)(x)=f(x)+g(x)[/tex]
So, in this case, you have
[tex]\begin{gathered} f(x)=-5^x-4 \\ g(x)=-3x-2 \\ (f+g)(x)=f(x)+g(x) \\ (f+g)(x)=(-5^x-4)+(-3x-2) \\ \text{ Remove parentheses} \\ (f+g)(x)=-5^x-4-3x-2 \\ \text{ Add like terms} \\ (f+g)(x)=-5^x-3x-6 \end{gathered}[/tex]
Therefore, the correct answer is B.
[tex](f+g)(x)=-5^x-3x-6[/tex]
