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

Answer: 0

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