Answer :
To find the value of [tex]\((f - g)(2)\)[/tex], we will proceed step-by-step, evaluating each function at [tex]\(x = 2\)[/tex] and then finding the difference.
Given:
[tex]\[ f(x) = 3x^2 + 1 \][/tex]
[tex]\[ g(x) = 1 - x \][/tex]
First, evaluate [tex]\(f(x)\)[/tex] at [tex]\(x = 2\)[/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]
Next, evaluate [tex]\(g(x)\)[/tex] at [tex]\(x = 2\)[/tex]:
[tex]\[ g(2) = 1 - 2 \][/tex]
[tex]\[ g(2) = -1 \][/tex]
Now, we need to find [tex]\( (f - g)(2) \)[/tex], which is [tex]\( f(2) - g(2) \)[/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]
So, the value of [tex]\( (f - g)(2) \)[/tex] is [tex]\( 14 \)[/tex].
Therefore, the correct answer is:
[tex]\[ \boxed{14} \][/tex]
Given:
[tex]\[ f(x) = 3x^2 + 1 \][/tex]
[tex]\[ g(x) = 1 - x \][/tex]
First, evaluate [tex]\(f(x)\)[/tex] at [tex]\(x = 2\)[/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]
Next, evaluate [tex]\(g(x)\)[/tex] at [tex]\(x = 2\)[/tex]:
[tex]\[ g(2) = 1 - 2 \][/tex]
[tex]\[ g(2) = -1 \][/tex]
Now, we need to find [tex]\( (f - g)(2) \)[/tex], which is [tex]\( f(2) - g(2) \)[/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]
So, the value of [tex]\( (f - g)(2) \)[/tex] is [tex]\( 14 \)[/tex].
Therefore, the correct answer is:
[tex]\[ \boxed{14} \][/tex]
