Answer :

To find the value of [tex]\( g(5) \)[/tex] given the functions [tex]\( f(x) = 3x + 3 \)[/tex] and [tex]\( g(x) = f(x) + 6 \)[/tex], follow these steps:

1. Evaluate [tex]\( f(5) \)[/tex]:
[tex]\[ f(x) = 3x + 3 \][/tex]
Substitute [tex]\( x = 5 \)[/tex] into the function [tex]\( f \)[/tex]:
[tex]\[ f(5) = 3(5) + 3 \][/tex]
Calculate the value:
[tex]\[ f(5) = 15 + 3 = 18 \][/tex]

2. Use the value of [tex]\( f(5) \)[/tex] to find [tex]\( g(5) \)[/tex]:
[tex]\[ g(x) = f(x) + 6 \][/tex]
Substitute [tex]\( x = 5 \)[/tex] into the function [tex]\( g \)[/tex]:
[tex]\[ g(5) = f(5) + 6 \][/tex]
Since [tex]\( f(5) = 18 \)[/tex], we can substitute this value:
[tex]\[ g(5) = 18 + 6 \][/tex]
Calculate the value:
[tex]\[ g(5) = 24 \][/tex]

Therefore, the value of [tex]\( g(5) \)[/tex] is [tex]\( \boxed{24} \)[/tex].