If $f: R \to R$ is defined by $f(x)=[2x]-2[x]$ for $x \in R,$ where $[x]$ is the greatest integer not exceeding x, then the range of f is :

Question

$$\begin {array} {1 1} (a)\;\{x \in R:0 \leq x \leq 1\} & \quad (b)\;\{0,1 \} \\ (c)\;\{x \in R : x > 0\} & \quad (d)\;\{x \in R: x \leq 0\} \end {array}$$