To find [tex]\((f + g)(x)\)[/tex], we need to sum the functions [tex]\(f(x)\)[/tex] and [tex]\(g(x)\)[/tex]. We are given:
[tex]\[ f(x) = 5x^2 + 9x - 4 \][/tex]
[tex]\[ g(x) = -8x^2 - 3x - 4 \][/tex]
Now, we sum [tex]\(f(x)\)[/tex] and [tex]\(g(x)\)[/tex] term by term.
1. Sum the [tex]\(x^2\)[/tex] terms:
[tex]\[ 5x^2 + (-8x^2) = 5x^2 - 8x^2 = -3x^2 \][/tex]
2. Sum the [tex]\(x\)[/tex] terms:
[tex]\[ 9x + (-3x) = 9x - 3x = 6x \][/tex]
3. Sum the constant terms:
[tex]\[ -4 + (-4) = -4 - 4 = -8 \][/tex]
Now, putting these results together, we get:
[tex]\[ (f + g)(x) = -3x^2 + 6x - 8 \][/tex]
Thus, the correct answer is:
[tex]\[ \boxed{-3x^2 + 6x - 8} \][/tex]
