To find [tex]\((f+g)(x)\)[/tex] given the functions [tex]\(f(x) = 3^x + 10\)[/tex] and [tex]\(g(x) = 2x - 4\)[/tex], we need to add these functions together. Let's proceed with the step-by-step solution.
Step 1: Write down the expressions for [tex]\(f(x)\)[/tex] and [tex]\(g(x)\)[/tex].
[tex]\[ f(x) = 3^x + 10 \][/tex]
[tex]\[ g(x) = 2x - 4 \][/tex]
Step 2: Add [tex]\(f(x)\)[/tex] and [tex]\(g(x)\)[/tex] to find [tex]\((f+g)(x)\)[/tex].
[tex]\[ (f+g)(x) = f(x) + g(x) \][/tex]
Step 3: Substitute the expressions for [tex]\(f(x)\)[/tex] and [tex]\(g(x)\)[/tex].
[tex]\[ (f+g)(x) = (3^x + 10) + (2x - 4) \][/tex]
Step 4: Combine like terms.
[tex]\[ (f+g)(x) = 3^x + 10 + 2x - 4 \][/tex]
[tex]\[ (f+g)(x) = 3^x + 2x + 6 \][/tex]
Therefore, the function [tex]\((f+g)(x)\)[/tex] simplifies to:
[tex]\[ (f+g)(x) = 3^x + 2x + 6 \][/tex]
So, the correct answer is:
A. [tex]\((f+g)(x) = 3^x + 2x + 6\)[/tex].
