Find the points of discontinuity for f(x) = IxI - Ix-1I(No hyperlinking,please!)

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Please find below the solution to the asked query:

$$\begin{gathered} \mathrm{f}\left(\mathrm{x}\right)=\left|\mathrm{x}\right|-\left|\mathrm{x}-1\right| \\ \mathrm{As} \mathrm{f}\left(\mathrm{x}\right) \mathrm{is} \mathrm{defined} \mathrm{for} \mathrm{all} \mathrm{real} \mathrm{values} \mathrm{of} \mathrm{x} \mathrm{and} \mathrm{modulus} \mathrm{function} \mathrm{does} \mathrm{not} \\ \mathrm{jump} \mathrm{in} \mathrm{its} \mathrm{domain}, \mathrm{hence} \mathrm{f}\left(\mathrm{x}\right) \mathrm{is} \mathrm{continuous} \mathrm{for} \mathrm{all} \mathrm{x}\in \mathrm{R} \mathrm{i}.\mathrm{e}. \mathrm{there} \mathrm{is} \\ \mathrm{no} \mathrm{point} \mathrm{of} \mathrm{discontinuity}. \end{gathered}$$

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