RU-ALLRUSSIAN 1974 Problem 15

f is a function on the closed interval [0, 1] with non- negative real values. $\mathrm{f}(1) = 1$ and $\mathrm{f}(\mathrm{x} + \mathrm{y}) \geq \mathrm{f}(\mathrm{x}) + \mathrm{f}(\mathrm{y})$ for all $\mathrm{x}, \mathrm{y}$ . Show that $\mathrm{f}(\mathrm{x}) \leq 2\mathrm{x}$ for all $\mathrm{x}$ . Is it necessarily true that $\mathrm{f}(\mathrm{x}) \leq 1.9\mathrm{x}$ for all $\mathrm{x}$ .