I'm just a bit confused as to how to prove these.

(5 marks) Throughout this question we work in (R, | . [). (a) (2 marks) Let x E R. Prove that translation by x, To : RaymatyER is a homeomorphism. (b) (3 marks) Let K be a compact subset of R, and U be an open set containing 0. Show that there exist X1, ..., n E K for which K C U._xit U, where xit U = {xi tu | u EU}. [Hint: x ( x + U for every x E K.]