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JEE Main202126 Aug 2021Evening ShiftMathematicsContinuity and DifferentiabilityActual

Let [ t ] denote the greatest integer less than or equal to t . Let f ( x ) = x - [ x ] , g ( x ) = 1 - x + [ x ] , and h ( x ) = min f ( x ) , g ( x ) , x ∈ [ - 2 , 2 ] . Then h is :

Options

  1. Acontinuous in [ - 2 , 2 ] but not differentiable at more than four points in ( - 2 , 2 )
  2. BContinous in [ - 2 , 2 ] but not differentiable at exactly three poionts in ( - 2 , 2 )
  3. Cnot continuous at exactly four points in [ - 2 , 2 ]
  4. Dnot continuous at exactly three points in [ - 2 , 2 ]

Correct answer

A. continuous in [ - 2 , 2 ] but not differentiable at more than four points in ( - 2 , 2 )

Step-by-step solution

f ( x ) = x - [ x ] = x g ( x ) = 1 - x + [ x ] = 1 - x Now, Graph of min f ( x ) , g ( x ) Clearly graph is continuous in [ - 2 , 2 ] but non differentiable at 7 points (i.e. greater than 4 ) in ( - 2 , 2 )

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