To solve for [tex]\((f+g)(x)\)[/tex] given the functions [tex]\(f(x) = 4x + 2\)[/tex] and [tex]\(g(x) = x^2 - 6\)[/tex], we need to add the two functions together. The combined function [tex]\( (f+g)(x) \)[/tex] is simply:
[tex]\[
(f+g)(x) = f(x) + g(x)
\][/tex]
Let’s substitute [tex]\(f(x)\)[/tex] and [tex]\(g(x)\)[/tex] into the equation:
[tex]\[
(f+g)(x) = (4x + 2) + (x^2 - 6)
\][/tex]
Now, combine like terms:
[tex]\[
(f+g)(x) = x^2 + 4x + 2 - 6
\][/tex]
Simplify the constant terms:
[tex]\[
(f+g)(x) = x^2 + 4x - 4
\][/tex]
Therefore, the combined function [tex]\((f+g)(x)\)[/tex] simplifies to:
[tex]\[
(f+g)(x) = x^2 + 4x - 4
\][/tex]
Thus, the correct answer is:
A. [tex]\( x^2 + 4x - 4 \)[/tex]
