How do you find (f o g)(x) and its domain, (g o f)(x) and its domain, (f o g)(-2) and (g o f)(-2) of the following problem ##f(x) = x^2 – 1##, ##g(x) = x + 1##?

Given
##color(white)(“XXX”)f(color(blue)(x))=color(blue)(x)^2-1##
and
##color(white)(“XXX”)g(color(red)(x))=color(red)(x)+1##
Note that ##(f@g)(x)## can be written ##f(g(x))##
and that ##(g@f)(x)## can be written ##g(f(x))##
##(f@g)(x) = f(color(blue)(g(x))) = color(blue)(g(x))^2-1##
##color(white)(“XXXXXX”)=(color(blue)(x+1))^2-1##
##color(white)(“XXXXXX”)=x^2+2x##
Since this is defined for all Real values of ##x##,
the of ##(f@g)(x)## is all Real values.
(although it wasn’t asked for, the would be ##[-1,+oo)##)
Similarly
##(g@f)(x)=g(color(red)(f(x)))+1##
##color(white)(“XXXXXX”)=g(color(red)(x^2-1))##
##color(white)(“XXXXXX”)=color(red)(x^2-1)+1##
##color(white)(“XXXXXX”)=x^2##
Again, this is defined for all Real values of ##x##
so the Domain is all Real values.
(but the Range is ##[0,+oo)##)