Real analysis problem on a continuously differentiable function that preserves volume.

3 . Definition : A transformation of class CF : IRS - R" is called volume pre- serving if for every cube CCR', with faces parallel to the coordinate planes , volume ( F ( C ) ) = volume ( C" ). ( 1 ) Show that { ( 2 , 4 , 2 ) = ( 2 + 3 , 2 - 4 , 2 2 - 4 ) is volume preserving . ( 11 ) Show that if G : 13 - R' is volume preserving then the determinant of its derivative G' equals II , and G maps open sets into open sets