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  • Let denote the greatest integer less than or equal to t. Let  <img alt="\\f\left ( x \right )= x-\left [ x \right ],g\

Let \left [ t \right ] denote the greatest integer less than or equal to t.
Let  \\f\left ( x \right )= x-\left [ x \right ],g\left ( x \right )= 1-x+\left [ x \right ],\, and\, h\left ( x \right )= min\left \{ f\left ( x \right ),g\left ( x \right ) \right \},x \in \left [ -2,2 \right ].Then h is :
Option: 1 continuous in [-2,2] but not differentiable at more than four points in (-2,2)
Option: 2 continuous in [-2,2] but not differentiable at exactly three  points in (-2,2)
Option: 3 not continuous at exactly four points in [-2,2]
Option: 4 not continuous at exactly three points in [-2,2]

Answers (1)

best_answer

f\left ( x \right )= x-\left [ x \right ]= \left \{ x \right \}

g\left ( x \right )= 1-\left ( x-\left [ x \right ] \right )= 1-\left \{ x \right \}

Using graphical tranformation, graph of y= g\left ( x \right )\, is



\therefore graph\, of\, h\left ( x \right )is


\therefore Continuous at each point but not differentiable at 7 points in (-2,2)

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Kuldeep Maurya

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