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 both |x| and \[\frac{|x|}{x}\] are discontinuous there
Correct Answer: C
Solution :
\[|x|\] is continuous at \[x=0\] and \[\frac{|x|}{x}\] is also discontinuous at \[x=0\] \ \[f(x)=\,|x|+\frac{|x|}{x}\] is discontinuous at \[x=0\].
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