To determine the value of [tex]\( g(8) \)[/tex], let us go through the steps in a detailed manner.
Given the functions:
[tex]\[ f(x) = 6x + 3 \][/tex]
[tex]\[ g(x) = f(x) + 6 \][/tex]
First, we need to evaluate [tex]\( f(8) \)[/tex].
1. Substitute [tex]\( x = 8 \)[/tex] into the function [tex]\( f(x) \)[/tex]:
[tex]\[ f(8) = 6(8) + 3 \][/tex]
[tex]\[ f(8) = 48 + 3 \][/tex]
[tex]\[ f(8) = 51 \][/tex]
Next, we use the value of [tex]\( f(8) \)[/tex] to find [tex]\( g(8) \)[/tex].
2. Substitute [tex]\( f(8) = 51 \)[/tex] into the function [tex]\( g(x) \)[/tex]:
[tex]\[ g(8) = f(8) + 6 \][/tex]
[tex]\[ g(8) = 51 + 6 \][/tex]
[tex]\[ g(8) = 57 \][/tex]
Therefore, the value of [tex]\( g(8) \)[/tex] is [tex]\( 57 \)[/tex].
[tex]\[
\boxed{57}
\][/tex]
