To solve for \( (f+g)(x) \) where \( f(x) = -5^x - 4 \) and \( g(x) = -3x - 2 \), we need to find the sum of these two functions:
1. Start with the functions given:
[tex]\[
f(x) = -5^x - 4
\][/tex]
[tex]\[
g(x) = -3x - 2
\][/tex]
2. To find \( (f+g)(x) \), we add \( f(x) \) and \( g(x) \):
[tex]\[
(f+g)(x) = f(x) + g(x)
\][/tex]
3. Substitute the expressions for \( f(x) \) and \( g(x) \) into the equation:
[tex]\[
(f+g)(x) = (-5^x - 4) + (-3x - 2)
\][/tex]
4. Combine the terms:
[tex]\[
(f+g)(x) = -5^x - 4 - 3x - 2
\][/tex]
5. Simplify the expression by combining the constants:
[tex]\[
(f+g)(x) = -5^x - 3x - 6
\][/tex]
Looking at the options provided:
A. \((f+g)(x) = -5^x - 7x - 2\)
B. \((f+g)(x) = 5^x + 3x + 6\)
C. \((f+g)(x) = -8x - 6\)
D. \((f+g)(x) = -5^x - 3x - 6\)
The correct answer matches the expression we derived:
[tex]\[
(f+g)(x) = -5^x - 3x - 6
\][/tex]
Therefore, the correct answer is:
[tex]\[
\boxed{D}
\][/tex]
