To solve for [tex]\((f - g)(2)\)[/tex] given [tex]\(f(x) = 3x^2 + 1\)[/tex] and [tex]\(g(x) = 1 - x\)[/tex], we follow these steps:
1. Calculate [tex]\(f(2)\)[/tex]:
[tex]\[
f(2) = 3(2)^2 + 1
\][/tex]
First, calculate [tex]\(2^2\)[/tex]:
[tex]\[
2^2 = 4
\][/tex]
Then multiply by 3:
[tex]\[
3 \cdot 4 = 12
\][/tex]
Finally, add 1:
[tex]\[
12 + 1 = 13
\][/tex]
So, [tex]\(f(2) = 13\)[/tex].
2. Calculate [tex]\(g(2)\)[/tex]:
[tex]\[
g(2) = 1 - 2
\][/tex]
Subtract 2 from 1:
[tex]\[
1 - 2 = -1
\][/tex]
So, [tex]\(g(2) = -1\)[/tex].
3. Calculate [tex]\((f - g)(2)\)[/tex]:
[tex]\[
(f - g)(2) = f(2) - g(2)
\][/tex]
Substitute the values we found:
[tex]\[
(f - g)(2) = 13 - (-1)
\][/tex]
Subtracting a negative is the same as adding:
[tex]\[
13 + 1 = 14
\][/tex]
Therefore, the value of [tex]\((f - g)(2)\)[/tex] is [tex]\(\boxed{14}\)[/tex].
