Determine whether the functions are inverses.
a. $f(x)=\frac{x+6}{2}$ and $g(x)=2(x-6)$

Step 1 ：Given two functions, $f(x)=\frac{x+6}{2}$ and $g(x)=2(x-6)$

Step 2 ：To determine if these functions are inverses of each other, we can compose the functions in both orders (f(g(x)) and g(f(x))) and see if the result is x in both cases.

Step 3 ：First, let's find f(g(x)). Substituting $g(x)=2(x-6)$ into $f(x)=\frac{x+6}{2}$, we get $f(g(x))=\frac{2(x-6)+6}{2}=x-3$

Step 4 ：Next, let's find g(f(x)). Substituting $f(x)=\frac{x+6}{2}$ into $g(x)=2(x-6)$, we get $g(f(x))=2(\frac{x+6}{2}-6)=x-6$

Step 5 ：The result of f(g(x)) is $x-3$ and the result of g(f(x)) is $x-6$. Since neither of these results is x, the functions f(x) and g(x) are not inverses of each other.

Step 6 ：$\boxed{{\displaystyle \text{The functions }f(x)=\frac{x+6}{2}\text{ and }g(x)=2(x-6)\text{ are not inverses of each other.}}}$