To find [tex]\( g(6) \)[/tex] for the function [tex]\( g(x) = 3|2x| \)[/tex]:
1. First, substitute [tex]\( x = 6 \)[/tex] into the function.
2. Calculate the expression inside the absolute value:
[tex]\[
g(6) = 3\left|2 \cdot 6\right|
\][/tex]
3. Simplify the multiplication inside the absolute value:
[tex]\[
g(6) = 3\left|12\right|
\][/tex]
4. The absolute value of 12 is 12:
[tex]\[
g(6) = 3 \cdot 12
\][/tex]
5. Multiply the result by 3:
[tex]\[
g(6) = 36
\][/tex]
Hence, the value of [tex]\( g(6) \)[/tex] is [tex]\( 36 \)[/tex].
