Question 1 of 25

If [tex] f(x) = -5^x - 4 [/tex] and [tex] g(x) = -3x - 2 [/tex], find [tex] (f+g)(x) [/tex].

A. [tex] (f+g)(x) = -5^x - 7x - 2 [/tex]
B. [tex] (f+g)(x) = 5^x + 3x + 6 [/tex]
C. [tex] (f+g)(x) = -8x - 6 [/tex]
D. [tex] (f+g)(x) = -5^x - 3x - 6 [/tex]



Answer :

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]