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Question
Let f (x) = | x | + | x − 1|, then
Options
f (x) is continuous at x = 0, as well as at x = 1
f (x) is continuous at x = 0, but not at x = 1
f (x) is continuous at x = 1, but not at x = 0
none of these
Solution
f (x) is continuous at x = 0, as well as at x = 1
Since modulus function is everywhere continuous ,
It is known that if f and g are continuous functions, then f + g will also be continuous.
Thus,
Hence,
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