The domain of every function #f(x)# is the set of #x#-values that are 'plugged' into the function #f#. It then follows that the domain of #f(u)# is the set of #u#-values plugged into the function #f#. Make the substitution #u=g(x)#. The domain of #g(x)# determines the set of #u#-values that are plugged into #f(x)#.
In short
Domain of #g(x)# –#(g)-># Range of #g(x)# = Domain of #f(u)# –#(f)-># Range of #f(u)# = Range of #f(g(x))#
Thus the domain of #f(g(x))# = set of #x#-values that are plugged into the #fg# function = set of #x#-values that are plugged into the #g# function = domain of #g(x)# = #x > -2# (for real values of #sqrt(2x+4)#, #2x+4>0 \Rightarrow x > -2#
