Triangle-Preserving Functions

Call $f$ triangle-preserving if, whenever $a, b, c$ lie in its domain and are the side lengths of some triangle, the values $f(a), f(b), f(c)$ are also the side lengths of some triangle. Which of the following are triangle-preserving?

1. $f(x) = \sqrt{x}$ (on $x > 0$); 2. $g(x) = \sin x$ on $(0, \pi)$; 3. $h(x) = \ln x$ on $[2, +\infty)$.