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Evaluate [tex] f(x) [/tex] when [tex] x = 6 [/tex].

[tex]
f(x) =
\begin{cases}
6x^2 + 2 & \text{if } -6 < x < 9 \\
12 & \text{if } 9 \leq x < 13
\end{cases}
[/tex]

A. 74
B. 12
C. 218
D. 6

Answer :

To evaluate [tex]\( f(x) \)[/tex] when [tex]\( x = 6 \)[/tex], we need to look at the definition of the function [tex]\( f(x) \)[/tex].

The function [tex]\( f(x) \)[/tex] is defined in two parts:

1. [tex]\( f(x) = 6x^2 + 2 \)[/tex] when [tex]\(-6 < x < 9\)[/tex]
2. [tex]\( f(x) = 12 \)[/tex] when [tex]\( 9 \leq x < 13 \)[/tex]

Since [tex]\( x = 6 \)[/tex] falls within the interval [tex]\(-6 < x < 9\)[/tex], we will use the first part of the function to find [tex]\( f(x) \)[/tex].

Let's calculate:

[tex]\[
f(x) = 6x^2 + 2
\][/tex]

Substitute [tex]\( x = 6 \)[/tex] into the expression:

[tex]\[
f(6) = 6(6)^2 + 2
\][/tex]

Calculate [tex]\( 6^2 \)[/tex]:

[tex]\[
6^2 = 36
\][/tex]

Then, substitute back into the expression:

[tex]\[
f(6) = 6 \times 36 + 2
\][/tex]

Now, calculate [tex]\( 6 \times 36 \)[/tex]:

[tex]\[
6 \times 36 = 216
\][/tex]

Add 2 to the result:

[tex]\[
216 + 2 = 218
\][/tex]

Therefore, [tex]\( f(6) = 218 \)[/tex].

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