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?