To determine [tex]\((f + g)(x)\)[/tex], we need to sum the functions [tex]\(f(x)\)[/tex] and [tex]\(g(x)\)[/tex].
Given:
[tex]\[
f(x) = 2x^2 + 1
\][/tex]
[tex]\[
g(x) = x^2 - 7
\][/tex]
First, let's add these two functions together:
[tex]\[
(f + g)(x) = f(x) + g(x)
\][/tex]
Substitute the expressions for [tex]\(f(x)\)[/tex] and [tex]\(g(x)\)[/tex]:
[tex]\[
(f + g)(x) = (2x^2 + 1) + (x^2 - 7)
\][/tex]
Next, combine like terms:
[tex]\[
(f + g)(x) = 2x^2 + x^2 + 1 - 7
\][/tex]
[tex]\[
(f + g)(x) = 3x^2 - 6
\][/tex]
So, the resulting function is:
[tex]\[
(f + g)(x) = 3x^2 - 6
\][/tex]
Therefore, the correct answer is:
D. [tex]\(3x^2 - 6\)[/tex]
