Suppose that f is continuous on [a, b]. Prove that given > 0 there exist points

Suppose that f is continuous on [a, b]. Prove that given ε > 0 there exist points x0 = a < x1 < ∙ ∙ ∙ < xn = b such that if Ek: = {y : f(x) = y for some x ∊ [xk-1, xk]}, then sup Ek - inf £k < ε for k = 1,2,..., n.