Please write as detail as you can, Thanks!

Please write clearly and detail steps Let (X, d) be a metric space and U be a connected subset of X. a ). Let f : X - R be a continuous function. Assuming that of f(U), prove that f(x) f(y) > 0 for all x, y E U. " b ) . Prove that if A C X and neither Un A, nor Un (X \\ A) is empty, then Un OA # 0