Consider this function:

\[ F(x) = \begin{cases} 1 - e^{-g(x)} & x\geq 0\\ 0 & \text{else}. \end{cases} \]

Assume \(g(x)\) is continuous. I want \(F(x)\) to be a continuous function, and I want \(F(x)\) to be a valid cumulative distribution function (CDF). What properties must \(g(x)\) satisfy in order to make that happen? Give three examples of \(g\) that have these properties.