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.