To solve the problem, we will follow these steps:
1. Step 1: Calculate [tex]\( f(6) \)[/tex]
The function [tex]\( f(x) \)[/tex] is defined as:
[tex]\[
f(x) = \frac{x}{2} + 5
\][/tex]
Substituting [tex]\( x = 6 \)[/tex] into the function [tex]\( f(x) \)[/tex]:
[tex]\[
f(6) = \frac{6}{2} + 5
\][/tex]
Simplifying the expression:
[tex]\[
f(6) = 3 + 5 = 8.0
\][/tex]
2. Step 2: Calculate [tex]\( g(f(6)) \)[/tex]
First, recall that we have already found [tex]\( f(6) = 8.0 \)[/tex].
Next, the function [tex]\( g(x) \)[/tex] is defined as:
[tex]\[
g(x) = 3x + 4
\][/tex]
So we need to find [tex]\( g(8.0) \)[/tex]:
[tex]\[
g(8.0) = 3(8.0) + 4
\][/tex]
Simplifying the expression:
[tex]\[
g(8.0) = 24.0 + 4 = 28.0
\][/tex]
Therefore, the value of [tex]\( g(f(6)) \)[/tex] is [tex]\( 28.0 \)[/tex].
