To find [tex]\((f+g)(x)\)[/tex], we need to add the functions [tex]\(f(x)\)[/tex] and [tex]\(g(x)\)[/tex] together.
Given:
[tex]\[ f(x) = 2x^2 + 1 \][/tex]
[tex]\[ g(x) = x^2 - 7 \][/tex]
The function [tex]\((f+g)(x)\)[/tex] is defined as:
[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]
Therefore, the correct expression for [tex]\((f+g)(x)\)[/tex] is:
[tex]\[ (f+g)(x) = 3x^2 - 6 \][/tex]
So, the correct answer is:
[tex]\[ \boxed{3x^2 - 6} \][/tex]
Which corresponds to option:
C. [tex]\(3x^2 - 6\)[/tex]
