Suppose that E Rn and that f: E Rm. a) Prove that f is continuous

Question:

Suppose that E ⊂ Rn and that f: E → Rm.
a) Prove that f is continuous on E if and only if f-1(B) is relatively closed in E for every closed subset B of Rm.
b) Suppose that f is continuous on E. Prove that if V is relatively open in f(E), then f-l (V) is relatively open in E, and if B is relatively closed in f(E), then f-l(B) is relatively closed in E.