To solve for [tex]\((f - g)(2)\)[/tex], we need to evaluate the functions [tex]\(f(x)\)[/tex] and [tex]\(g(x)\)[/tex] at [tex]\(x = 2\)[/tex] and then find the difference.
First, let's evaluate [tex]\(f(x)\)[/tex] at [tex]\(x = 2\)[/tex]:
[tex]\[ f(x) = 3x^2 + 1 \][/tex]
Substitute [tex]\(x = 2\)[/tex]:
[tex]\[ f(2) = 3(2)^2 + 1 \][/tex]
[tex]\[ f(2) = 3(4) + 1 \][/tex]
[tex]\[ f(2) = 12 + 1 \][/tex]
[tex]\[ f(2) = 13 \][/tex]
Next, let's evaluate [tex]\(g(x)\)[/tex] at [tex]\(x = 2\)[/tex]:
[tex]\[ g(x) = 1 - x \][/tex]
Substitute [tex]\(x = 2\)[/tex]:
[tex]\[ g(2) = 1 - 2 \][/tex]
[tex]\[ g(2) = -1 \][/tex]
Now, we find [tex]\((f - g)(2)\)[/tex]:
[tex]\[ (f - g)(2) = f(2) - g(2) \][/tex]
Substitute the values we calculated:
[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]
