MathDB
IMC 2006, problem 1, day 1

Source: Easy

July 22, 2006
IMCcollege contests

Problem Statement

Let f:Rā†’Rf: \mathbb{R}\to \mathbb{R} be a real function. Prove or disprove each of the following statements. (a) If f is continuous and range(f)=R\mathbb{R} then f is monotonic (b) If f is monotonic and range(f)=R\mathbb{R} then f is continuous (c) If f is monotonic and f is continuous then range(f)=R\mathbb{R}
Back to ProblemsView on AoPS