To determine [tex]\((f+g)(x)\)[/tex] given the functions [tex]\( f(x) = x^2 - 3x - 4 \)[/tex] and [tex]\( g(x) = x^2 + x \)[/tex], we need to sum these two functions.
Starting with the functions:
[tex]\[ f(x) = x^2 - 3x - 4 \][/tex]
[tex]\[ g(x) = x^2 + x \][/tex]
Now, let's find [tex]\((f + g)(x)\)[/tex]:
[tex]\[ (f + g)(x) = f(x) + g(x) \][/tex]
[tex]\[ (f + g)(x) = (x^2 - 3x - 4) + (x^2 + x) \][/tex]
Next, we combine like terms:
[tex]\[ (f + g)(x) = x^2 + x^2 - 3x + x - 4 \][/tex]
[tex]\[ (f + g)(x) = 2x^2 - 2x - 4 \][/tex]
So, the function [tex]\((f + g)(x)\)[/tex] simplifies to:
[tex]\[ 2x^2 - 2x - 4 \][/tex]
Thus, the correct answer is:
[tex]\[ \boxed{2 x^2 - 2 x - 4} \][/tex]
