measure theory - How to determine if a random variable is $mathcal F$-measurable?

For example :

Consider the state space $\Omega = \mathbb{R}$, the $\sigma$-algebra, $\mathcal{F} = \{(-\infty, 0], (0, \infty), 0, \mathbb{R}\}$ and the random variable $X : \Omega \rightarrow \mathbb{R}$ defined by
$$\begin{align*} X(\omega) = \begin{cases} 3 & \omega < 0\\ 5 & \omega \geq 0 \end{cases} \end{align*}$$
Is $X$ $\mathcal{F}$-measurable?