Let f: [- 1,3] → R be defined as f(x) = \ array ll |x| + [x], x +...

f\left(x\right) = \left\{$\begin{array}{ll}\left|x\right| + \left[x\right]; - 1 \le x < 1 \\ x + \left|x\right|; 1 \le x < 2 \\ \left|x\right| + \left[x\right]; 2 \le x \le 3\end{array}$\right)</p><p>= \left\{$$\begin{array}{ll}- x - 1; - 1 \le x < 0 \\ x + 0; 0 \le x < 1 \\ 2x; 1 \le x < 2 \\ x + 2; 2 \le x < 3 \\ 6; x = 3\end{array}$$\right)

At $x = 0, 1, 2, 3$ $f$ changes its definition.

$∴$ At $x = 0LHL = - 1, RHL = 0 ⇒ f$ is discontinuous at

$x = 0$

$x = 1LHL = 1, RHL = 2 ⇒ f$ is discontinuous at $x = 1$

$x = 2LHL = RHL = f\left(2\right) = 4 ⇒ f$ is continuous at $x = 2$

$x = 3LHL = 5, f\left(3\right) = 6 ⇒ f$ is discontinuous at $x = 1$

$∴$ Points of discontinuity are $0, 1, 3 .$