Let f : R R be defined by f(x) = cosx. Let A = [/2,/2] and B = {0}.

(i) (4 marks) Find f(A) and f1(B).

(ii) (4 marks) Write down an example of an open set U such that f(U) is not open. Write down an example of a compact set C such that f1(C) is not compact. You need only write these down: there is no need to verify the statements. (Here, the metric on R is the usual Euclidean metric.)