Let f (x) = | x | + | x − 1|, then

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f (x) is continuous at x = 0, as well as at x = 1 Since modulus function is everywhere continuous , \left| x ight| 	ext{ and } \left| x - 1 ight| are also everywhere continuous. Also, It is known that if f and g are continuous functions, then f + g will also be continuous. Thus, ​ ​ \left| x ight| + \left| x - 1 ight| is everywhere continuous. Hence, f\left( x ight) is continuous at x = 0 	ext{ and } x = 1

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