To find the value of [tex]\((f - g)(2)\)[/tex] when [tex]\(f(x) = 3x^2 + 1\)[/tex] and [tex]\(g(x) = 1 - x\)[/tex], let's go through it step-by-step.
1. Evaluate [tex]\(f(2)\)[/tex]:
Given [tex]\(f(x) = 3x^2 + 1\)[/tex],
[tex]\[
f(2) = 3(2)^2 + 1 = 3 \cdot 4 + 1 = 12 + 1 = 13.
\][/tex]
2. Evaluate [tex]\(g(2)\)[/tex]:
Given [tex]\(g(x) = 1 - x\)[/tex],
[tex]\[
g(2) = 1 - 2 = -1.
\][/tex]
3. Calculate [tex]\((f - g)(2)\)[/tex]:
[tex]\[
(f - g)(2) = f(2) - g(2).
\][/tex]
Substitute the values found:
[tex]\[
(f - g)(2) = 13 - (-1) = 13 + 1 = 14.
\][/tex]
Hence, the value of [tex]\((f - g)(2)\)[/tex] is [tex]\(\boxed{14}\)[/tex].
