The set of all points of continuous of fofof, where f(x) = sgn(x) is

$$\begin{gathered} \mathrm{f}\left(\mathrm{x}\right)=sgn \left(x\right) \\ =\left\{\begin{array}{ll}-1 \mathrm{if} & \mathrm{x}<0\\ 0 \mathrm{if}& \mathrm{x}=0\\ 1 \mathrm{if}& \mathrm{x}>0\end{array}\right. \\ \therefore \mathrm{f}\left(\mathrm{x} \right)\mathrm{is} \mathrm{discontinuous} \mathrm{at} \mathrm{x}=0 \\ \Rightarrow \mathrm{f} \mathrm{of} \mathrm{of} \mathrm{is} \mathrm{continuous} \mathrm{in} \mathrm{R}-\left\{0\right\} \end{gathered}$$