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Most Important Selected Qs for JEE AdvancedMathematicsContinuity and Differentiability

Let f: R R and g:(-2,2) R be two functions defined by f(x)= mat, (1-|x| , x^3+1 ) and g(x)=[f(x)] . Identify which of the following statement(s) is(arc) correct? [Note: [y] denotes greatest integer function less than or equal to y .]

Options

  1. ANumber of points where f(x) is discontinuous is 0 .
  2. BNumber of points where f(x) is non-derivable is 2 .
  3. CNumber of points where g(x) is discontinuous is 9 .
  4. DNumber of points where g(x) is non-derivable is 8 .

Correct answer

D. Number of points where g(x) is non-derivable is 8 .

Step-by-step solution

Clearly, f(x) is continuous everywhere but non-derivable at x=-1 only. g(x) is discontinuous and non-derivable at exactly 8 points.

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