Sure, let's determine [tex]\((f+g)(2)\)[/tex] given the functions [tex]\( f(x) = 2x^2 + 3x \)[/tex] and [tex]\( g(x) = x - 2 \)[/tex].
First, let's break down the process step-by-step:
Step 1: Evaluate [tex]\( f(x) \)[/tex] at [tex]\( x = 2 \)[/tex]
[tex]\[ f(2) = 2 \cdot (2)^2 + 3 \cdot (2) \][/tex]
[tex]\[ f(2) = 2 \cdot 4 + 6 \][/tex]
[tex]\[ f(2) = 8 + 6 \][/tex]
[tex]\[ f(2) = 14 \][/tex]
Step 2: Evaluate [tex]\( g(x) \)[/tex] at [tex]\( x = 2 \)[/tex]
[tex]\[ g(2) = 2 - 2 \][/tex]
[tex]\[ g(2) = 0 \][/tex]
Step 3: Combine the results of [tex]\( f(2) \)[/tex] and [tex]\( g(2) \)[/tex] to find [tex]\((f+g)(2)\)[/tex]
[tex]\[ (f+g)(2) = f(2) + g(2) \][/tex]
[tex]\[ (f+g)(2) = 14 + 0 \][/tex]
[tex]\[ (f+g)(2) = 14 \][/tex]
So, the correct answer is [tex]\( \boxed{14} \)[/tex].
