Question

Find the number of points of discontinuity of the function
$f(x)=|x|+\left|\frac{x}{3}-1\right|+|| x|-| \frac{x}{3}-1||$ in $x \in(-\infty, \infty)$

Answer 1

Define $f(x)=\begin{cases}-2 x ; & -\infty< x< \frac{-3}{2} \\ 2-\frac{2 x}{3} ; & \frac{-3}{2} \leq x \leq \frac{3}{4} \\ 2 x ; & \frac{3}{4} < x< \infty\end{cases}$
So, $f(x)$ is continuous for all $x \in R$.