Find the discontinuity

$$\begin{gathered} \mathrm{Dear} \mathrm{student}, \\ \mathrm{We} \mathrm{know} \mathrm{that}, \\ \mathrm{x}=\left[\mathrm{x}\right]+\left\{\mathrm{x}\right\} \\ \left\{\mathrm{x}\right\}=\mathrm{x}-\left[\mathrm{x}\right] \\ \mathrm{So}, \mathrm{g}\left(\mathrm{x}\right)=\left\{\mathrm{x}\right\} \end{gathered}$$

Above graph is of {x}.
It is discontinuous at every integral point.
Option C is correct.
Regards