Given any functions f:X to Y and g:A to B, is the function h(x)=f(g(x)) well defined for any elements x in g⁻¹(X ∩ g[A])? Can we write h=f° g? Or is the composition of f and g only defined when the domain of g equals the codomain of f? If the composition is still well defined for some values, then why limit the definition? Does the possibility of functions with empty domains pose a problem? Would it still be valid to write h=f° g?