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If [tex]\( f(x) = 3x^2 + 1 \)[/tex] and [tex]\( g(x) = 1 - x \)[/tex], what is the value of [tex]\( (f - g)(2) \)[/tex]?

A. 12
B. 14
C. 36
D. 38

Sagot :

GinnyAnswer
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]
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