See the explanation:
Explanation:
Here we have two functions:
[tex]f(x)=2x+6 \ and \ g(x)=\frac{1}{2}x+2[/tex]
So we need to perform the following function compositions:
Case 1.
[tex]f(g(6))=? \\ \\ \\ First \ of \ all: \\ \\ f(g(x))=2(\frac{1}{2}x+2)+6 \\ \\ f(g(x))=x+4+6 \\ \\ f(g(x))=x+10 \\ \\ \\ So: \\ \\ f(g(x))=6+10 \\ \\ \boxed{f(g(6))=16}[/tex]
Case 2.
[tex]g(f(6))=? \\ \\ \\ First \ of \ all: \\ \\ g(f(x))=\frac{1}{2}(2x+6)+2 \\ \\ g(f(x))=x+3+2 \\ \\ g(f(x))=x+5 \\ \\ \\ So: \\ \\ g(f(6))=6+5 \\ \\ \boxed{g(f(6))=11}[/tex]
Case 3.
This was calculated in case 1:
[tex]f(g(x))=x+10[/tex]
Case 4.
This was calculated in case 3:
[tex]g(f(x))=x+5[/tex]
Learn more:
Inverse functions: https://brainly.com/question/12253822
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