A) continuous at the origin
B) discontinuous at the origin because \[|x|\] is discontinuous there
C) discontinuous at the origin because \[\frac{|x|}{x}\] is discontinuous there
D) discontinuous at the origin because \[|x|\] and \[\frac{|x|}{x}\]are discontinuous there
Correct Answer: B
Solution :
\[|x|\]is continuous at \[x=0\]and \[\frac{|x|}{x}\]is, also discontinuous at \[x=0.\] \[\therefore \]\[f(x)=|x|+\frac{|x|}{x}\]is discontinuous at \[x=0.\]
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