Katherine00123idn
Answered

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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][tex]$(f - g)(2)$[/tex][/tex]?

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

Sagot :

GinnyAnsweridn
Let's find the value of [tex]\((f-g)(2)\)[/tex] step by step.

Given the functions:
[tex]\[ f(x) = 3x^2 + 1 \][/tex]
[tex]\[ g(x) = 1 - x \][/tex]

We are tasked with finding the value of [tex]\((f - g)(2)\)[/tex].

First, we need to evaluate [tex]\(f(2)\)[/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, we evaluate [tex]\(g(2)\)[/tex]:

[tex]\[ g(2) = 1 - 2 \][/tex]
[tex]\[ g(2) = -1 \][/tex]

Now, we calculate [tex]\((f - g)(2)\)[/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]

Therefore, the value of [tex]\((f - g)(2)\)[/tex] is [tex]\(\boxed{14}\)[/tex].
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