Sure, let’s walk through each step to find the correct expression for [tex]\((f+g)(x)\)[/tex].
The functions given are:
[tex]\[ f(x) = -5^x - 4 \][/tex]
[tex]\[ g(x) = -3x - 2 \][/tex]
The combined function [tex]\( (f + g)(x) \)[/tex] is defined as the sum of [tex]\( f(x) \)[/tex] and [tex]\( g(x) \)[/tex]:
[tex]\[ (f + g)(x) = f(x) + g(x) \][/tex]
Let's substitute the expressions for [tex]\( f(x) \)[/tex] and [tex]\( g(x) \)[/tex]:
[tex]\[ (f + g)(x) = (-5^x - 4) + (-3x - 2) \][/tex]
We can simplify this by combining like terms:
[tex]\[ (f + g)(x) = -5^x - 4 - 3x - 2 \][/tex]
[tex]\[ (f + g)(x) = -5^x - 3x - 4 - 2 \][/tex]
[tex]\[ (f + g)(x) = -5^x - 3x - 6 \][/tex]
So, the correct expression for [tex]\((f + g)(x)\)[/tex] is:
[tex]\[ (f + g)(x) = -5^x - 3x - 6 \][/tex]
Hence, the correct choice is:
A. [tex]\( (f + g)(x) = -5^x - 3x - 6 \)[/tex]
