To find the value of [tex]\((f - g)(2)\)[/tex] where [tex]\(f(x) = 3x^2 + 1\)[/tex] and [tex]\(g(x) = 1 - x\)[/tex], we need to perform the following steps:
1. Calculate [tex]\(f(2)\)[/tex]:
[tex]\[
f(x) = 3x^2 + 1
\][/tex]
Substitute [tex]\(x = 2\)[/tex] into the function [tex]\(f(x)\)[/tex]:
[tex]\[
f(2) = 3(2)^2 + 1 = 3 \cdot 4 + 1 = 12 + 1 = 13
\][/tex]
2. Calculate [tex]\(g(2)\)[/tex]:
[tex]\[
g(x) = 1 - x
\][/tex]
Substitute [tex]\(x = 2\)[/tex] into the function [tex]\(g(x)\)[/tex]:
[tex]\[
g(2) = 1 - 2 = -1
\][/tex]
3. Evaluate [tex]\((f - g)(2)\)[/tex]:
[tex]\[
(f - g)(x) = f(x) - g(x)
\][/tex]
Substitute [tex]\(x = 2\)[/tex], [tex]\(f(2)\)[/tex], and [tex]\(g(2)\)[/tex] into the expression:
[tex]\[
(f - g)(2) = f(2) - g(2) = 13 - (-1) = 13 + 1 = 14
\][/tex]
Thus, the value of [tex]\((f - g)(2)\)[/tex] is [tex]\(14\)[/tex].
The correct answer is [tex]\(\boxed{14}\)[/tex].
