Problem 565
Prove that if \(\displaystyle I\) is an interval and \(\displaystyle f:I\to\R\) is continuous and injective, then strictly monotone. Difficulty: 2. |
Problem 569
Is it true that if for the function \(\displaystyle f:\R\to\R\) we have \(\displaystyle \forall x\in\R~f(x-0)\le f(x)\le f(x+0)\), then\(\displaystyle f\) is monotone increasing? Difficulty: 8. |
Supported by the Higher Education Restructuring Fund allocated to ELTE by the Hungarian Government |