[tex]\bf \begin{cases}
f(x)=x^2-3\\
g(x)=\sqrt{3+x}
\end{cases}\\\\
-------------------------------\\\\
f(~~g(x)~~)=[g(x)]^2-3\implies f(~~g(x)~~)=[\sqrt{3+x}]^2-3
\\\\\\
f(~~g(x)~~)=3+x-3\implies \boxed{f(~~g(x)~~)=x}\\\\
-------------------------------\\\\
g(~~f(x)~~)=\sqrt{3+[f(x)]}\implies g(~~f(x)~~)=\sqrt{3+[x^2-3]}
\\\\\\
g(~~f(x)~~)=\sqrt{3+x^2-3}\implies g(~~f(x)~~)=\sqrt{x^2}
\\\\\\
\boxed{g(~~f(x)~~)=x}[/tex]
