Composition of function:

Given functiond f and g ,the composition of f and g denoted by 'fog' is the function defined by -
        (fog)(x)=f(g(x))         ;     (gof)(x)=g(f(x))

The domain of fog is defined to consist of all x and domain of g for which g(x) is the domain of f(x).

Example::

 here, f(x)=x^2+3
          g(x)=Sqrt[x]

 Now, (fog)(x)=f(g(x))
                       =f(Sqrt[x])
                       =x+3

 domain of g=[0,+Infinity)
 domain of fog=[0,+Infinity)


Again , (gof)(x)=g(f(x))
                         =g(x^2+3)
                         =Sqrt(x^2+3)
             
  domain of , f=(-Infinity,+Infinity)
  domain of ,gof=(-Infinity,+Infinity)