Given f(x)=|x−1|+|x+1|. Then f(x) is
continuous everywhere
Given function is,
f(x)=|x−1|+|x+1|
for x<−1
f(x)=1−x−x−1
=−2x
for −1<x<1
f(x)=1−x+x+1
=2
for x>1
f(x)=x−1+x+1
=2x
∴ The function can be drawn as below
From this its clear that the function is not discontinuous at any point.