Question

Find all the points of discontinuity of f(x) defined by f(x)=|x|-|x+1|.

Answer 1

Let g(x) =|x| and h(x) = |x+1|

Now, g(x) =|x| is the absolute valued function, so it is continuous function for all $xϵR$

h(x)=|x|+1 is the absolute valued function, so it is a continuous function for all $xϵR$

Since, g(x) and h(x) are both continuous functions for all $xϵR$ so, difference of two continuous function is a continuous function for all $xϵR$
Thus, f(x) =con$\left(x^2\right)$ is a continuous function at all points.

Hence, there is no point at which f(x) is discontinuous.