Function f(x) = * 20 c sgn ( [ x ] ) , , , ,; , , ,x I [ sgn ( x … - Vidyadip

MCQ

Function $f(x) = \left\{ {\begin{array}{*{20}{c}} {sgn \left( {\left[ x \right]} \right)\,\,\,\,;\,\,\,x \ne I} \\ {\left[ {sgn \left( x \right)} \right]\,\,\,;\,\,\,x = I} \end{array}} \right.$ is '( where $sgn ()$ denotes signum function $and$ $[.]$ denotes greatest integer function )

A
Continuous but not differentiable at $x = 2$
B
Discontinuous at every integer
✓
Non differentiable at $x = 0\,\,and\,\,1$ only
D
Non differentiable at every natural number

✓

Answer

Correct option: C.

Non differentiable at $x = 0\,\,and\,\,1$ only

c

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