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Question: Answered & Verified by Expert
If $f(x)=|x|/x$ for x≠0 and 1 for X=0, then the function is
MathematicsContinuity and DifferentiabilityMHT CETMHT CET 2020 (16 Oct Shift 2)
Options:
  • A continuous but not differentiable at $x=0$
  • B differentiable but not continuous at $x=0$
  • C neither continuous nor differentiable at $x=0$
  • D continuous and differentiable at $x=0$
Solution:
1832 Upvotes Verified Answer
The correct answer is: neither continuous nor differentiable at $x=0$
$f(x)=\left\{\begin{array}{cc}
1 & x>0 \\
-1 & x < 0 \\
1 & x=0
\end{array}\right.$
So function discontinuous and non differentiable

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