To determine the value of [tex]\((f - g)(2)\)[/tex], let's follow these steps:
1. Define the functions [tex]\(f(x)\)[/tex] and [tex]\(g(x)\)[/tex]:
[tex]\[ f(x) = 3x^2 + 1 \][/tex]
[tex]\[ g(x) = 1 - x \][/tex]
2. Evaluate [tex]\(f(2)\)[/tex]:
[tex]\[ f(2) = 3(2)^2 + 1 \][/tex]
[tex]\[ f(2) = 3 \cdot 4 + 1 \][/tex]
[tex]\[ f(2) = 12 + 1 \][/tex]
[tex]\[ f(2) = 13 \][/tex]
3. Evaluate [tex]\(g(2)\)[/tex]:
[tex]\[ g(2) = 1 - 2 \][/tex]
[tex]\[ g(2) = -1 \][/tex]
4. Find [tex]\((f - g)(2)\)[/tex]:
[tex]\[ (f - g)(2) = f(2) - g(2) \][/tex]
[tex]\[ (f - g)(2) = 13 - (-1) \][/tex]
[tex]\[ (f - g)(2) = 13 + 1 \][/tex]
[tex]\[ (f - g)(2) = 14 \][/tex]
Therefore, the value of [tex]\((f - g)(2)\)[/tex] is [tex]\(\boxed{14}\)[/tex].
