Answer :
To evaluate [tex]\( f(x) \)[/tex] when [tex]\( x = 6 \)[/tex], follow these steps:
1. Identify the appropriate condition: We need to choose the correct piece of the piecewise function based on the value of [tex]\( x \)[/tex].
- The function [tex]\( f(x) \)[/tex] has the condition [tex]\( -6 < x < 9 \)[/tex].
- Since [tex]\( x = 6 \)[/tex], which falls within this range, we'll use the corresponding expression.
2. Use the expression for [tex]\( -6 < x < 9 \)[/tex]:
[tex]\[
f(x) = 6x^2 + 2
\][/tex]
3. Substitute [tex]\( x = 6 \)[/tex] into the expression:
- First, calculate [tex]\( 6^2 \)[/tex]:
[tex]\[
6^2 = 36
\][/tex]
- Multiply by 6:
[tex]\[
6 \times 36 = 216
\][/tex]
- Add 2:
[tex]\[
216 + 2 = 218
\][/tex]
4. Result: Therefore, when [tex]\( x = 6 \)[/tex], the value of the function [tex]\( f(x) \)[/tex] is [tex]\( 218 \)[/tex].
1. Identify the appropriate condition: We need to choose the correct piece of the piecewise function based on the value of [tex]\( x \)[/tex].
- The function [tex]\( f(x) \)[/tex] has the condition [tex]\( -6 < x < 9 \)[/tex].
- Since [tex]\( x = 6 \)[/tex], which falls within this range, we'll use the corresponding expression.
2. Use the expression for [tex]\( -6 < x < 9 \)[/tex]:
[tex]\[
f(x) = 6x^2 + 2
\][/tex]
3. Substitute [tex]\( x = 6 \)[/tex] into the expression:
- First, calculate [tex]\( 6^2 \)[/tex]:
[tex]\[
6^2 = 36
\][/tex]
- Multiply by 6:
[tex]\[
6 \times 36 = 216
\][/tex]
- Add 2:
[tex]\[
216 + 2 = 218
\][/tex]
4. Result: Therefore, when [tex]\( x = 6 \)[/tex], the value of the function [tex]\( f(x) \)[/tex] is [tex]\( 218 \)[/tex].
