MathNet 1974 — Part 01 Question 12

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