To solve [tex]\( f[g(6)] \)[/tex], let's follow the steps methodically:
1. Evaluate [tex]\( g(6) \)[/tex]:
Given the function [tex]\( g(x) = x - 8 \)[/tex], we substitute [tex]\( x \)[/tex] with 6:
[tex]\[
g(6) = 6 - 8 = -2
\][/tex]
2. Evaluate [tex]\( f(g(6)) \)[/tex]:
Next, we need to use the result from [tex]\( g(6) \)[/tex] in the function [tex]\( f(x) \)[/tex].
Given the function [tex]\( f(x) = 6x + 12 \)[/tex], we substitute [tex]\( x \)[/tex] with the value of [tex]\( g(6) \)[/tex], which we found to be [tex]\(-2\)[/tex]:
[tex]\[
f(-2) = 6(-2) + 12 = -12 + 12 = 0
\][/tex]
Therefore, the solution for [tex]\( f[g(6)] \)[/tex] is:
[tex]\[
f[g(6)] = 0
\][/tex]
Thus, the correct answer is [tex]\( 0 \)[/tex].
