Evaluate composite functions 2

$\begin{aligned} g(f({\color{#3D99F6}6})) & = g\left(3\cdot 2^{{\color{#3D99F6}6}-8}\right) = g\left(3\cdot 2^{-2}\right) = g\left({\color{#D61F06}\frac 34}\right) = \frac 1{2\left( 1+ {\color{#D61F06}\frac 34} \right)} = \frac 27 \end{aligned}$

$\implies a+b = 2+7 = \boxed{9}$

Given that,

$f(x) = 3.2^{x-8}$

$g(x) = \dfrac{1}{2(1+x)}$

$g(f(6)) =?$

Now,

$f(6) = 3.2^{6-8}$

$= 3.2^{-2}$

$= \dfrac{3}{2^2}$

$=\dfrac34$

Again,

$g \left( \dfrac{3}{4} \right) = \dfrac{1}{2 (1+ 3/4 )}$

$= \left( \dfrac{1}{2(4+3)/4} \right)$

$= \dfrac{1}{2 (7/4)}$

$= \dfrac{1}{14/4}$

$= \dfrac{1}{7/2}$

$= \dfrac{2}{7}$

Therefore, the answer is $2 + 7 = 9$