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].
