[tex]\bf \begin{cases}
f(x)=x^2+3\\\\
g(x)=x+\cfrac{4}{3}
\end{cases}
\\\\\\
\boxed{x=2}\qquad g(2)=(2)+\cfrac{4}{3}\implies \boxed{g(2)=\cfrac{10}{3}}
\\\\\\
f(~~g(x)~~)=[g(x)]^2+3\implies f(~~g(2)~~)=[g(2)]^2+3
\\\\\\
f(~~g(2)~~)=\left[ \boxed{\frac{10}{3}} \right]^2+3\implies f(~~g(2)~~)=\cfrac{10^2}{3^2}+3
\\\\\\
f(~~g(2)~~)=\cfrac{100}{9}+3\implies f(~~g(2)~~)=\cfrac{100+27}{9}
\\\\\\
f(~~g(2)~~)=\cfrac{127}{9}[/tex]
