Question 1167404
Not fg(x).  If you are stating function composition then f(g(x)).


#1


You ask about domain.
{{{f(g(x))=2-(sqrt(x+2))^2}}}

{{{f(g(x))=2-(x+2)}}}

{{{f(g(x))=2-x-2}}}

{{{f(g(x))=2-2-x}}}

{{{f(g(x))=-x}}}
But look again at the original composition.  Necessary is  {{{x>=-2}}}.  Otherwise, f(g(x)) not a "Real" number.