Let's first understand what it means to find [tex]\((f+g)(x)\)[/tex]. The notation [tex]\((f+g)(x)\)[/tex] represents the sum of the functions [tex]\(f(x)\)[/tex] and [tex]\(g(x)\)[/tex]. To do this, we will add the expressions for [tex]\(f(x)\)[/tex] and [tex]\(g(x)\)[/tex] directly.
Given:
[tex]\[ f(x) = 3^x + 10 \][/tex]
[tex]\[ g(x) = 2x - 4 \][/tex]
To find [tex]\((f+g)(x)\)[/tex], we need to add [tex]\(f(x)\)[/tex] and [tex]\(g(x)\)[/tex]:
[tex]\[
(f+g)(x) = f(x) + g(x)
\][/tex]
Substitute the given expressions for [tex]\(f(x)\)[/tex] and [tex]\(g(x)\)[/tex]:
[tex]\[
(f+g)(x) = (3^x + 10) + (2x - 4)
\][/tex]
Combine like terms:
[tex]\[
(f+g)(x) = 3^x + 10 + 2x - 4
\][/tex]
Simplify the equation by combining the constant terms [tex]\(10-4\)[/tex]:
[tex]\[
(f+g)(x) = 3^x + 2x + 6
\][/tex]
Thus, the expression for [tex]\((f+g)(x)\)[/tex] is:
[tex]\[ (f+g)(x) = 3^x + 2x + 6 \][/tex]
Therefore, the correct answer is:
[tex]\[ \boxed{3^x + 2x + 6} \][/tex]
This corresponds to option A:
[tex]\[ \boxed{(f+g)(x) = 3^x + 2x + 6} \][/tex]
