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The function f(x) = |x|+(|x|)/(x) is...

The function `f(x) = |x|+(|x|)/(x) ` is

A

continuous at x = 0

B

discontinuous at the origin because |x| is discontinuous there

C

discontinuous at the origin because `(|x|)/(x)` is discontinuous there

D

discontinuous at the origin because both |x| and `(|x|)/(x)` are discontinuous there

Text Solution

Verified by Experts

The correct Answer is:
C
Since, |x| is continuous at x = 0 but `(|x|)/(x) ` is discontinuous at x = 0.
`therefore f(x)=|x|+(|x|)/(x)` is discontinuous at x = 0.
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