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Question

If function if $$f(x)=\left| x \right| +\left| x-1 \right| +\left| x-2 \right| $$, then it is-


A
Discontinuous at x=0
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B
Discontinuous at x=0,1
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C
Discontinuous at x=0,1,2
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D
Every where continuous
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Solution

The correct option is C Every where continuous
$$f(x)=\left| x \right| +\left| x-1 \right| +\left| x-2 \right| $$
See the graph of $$f(x)$$ clearly it is continuous $$\forall x$$
366747_284778_ans_69bdb8aacb724d0a8cbcfc92704cfb28.png

Mathematics

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