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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] 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].
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