High School

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]

Answer :

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

1. First part of the function: [tex]\( f(x) = 6x^2 + 2 \)[/tex] if [tex]\(-6 < x < 9\)[/tex].

2. Second part of the function: [tex]\( f(x) = 12 \)[/tex] if [tex]\( 9 \leq x < 13\)[/tex].

Since [tex]\( x = 6 \)[/tex] falls within the range [tex]\(-6 < x < 9\)[/tex], the first part of the function applies. Therefore, we use the equation [tex]\( f(x) = 6x^2 + 2 \)[/tex].

Let's calculate [tex]\( f(6) \)[/tex]:

- Substitute [tex]\( x = 6 \)[/tex] into [tex]\( 6x^2 + 2 \)[/tex]:

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

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

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

- Multiply by 6:

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

- Add 2:

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

Therefore, the value of [tex]\( f(6) \)[/tex] is 218.