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Most Important Selected Qs for JEE AdvancedMathematicsContinuity and Differentiability

Let f(x)=|x-1|([x]-[-x]) , then which of the following statement(s) is/are correct? (where [ x ] denotes greatest integer function)

Options

  1. Af(x) is continuous at x=1
  2. Bf(x) is derivable at x=1
  3. Cf(x) is non-derivable at x=1
  4. Df(x) is discontinuous at x=1

Correct answer

C. f(x) is non-derivable at x=1

Step-by-step solution

We have . f^ (1⁺ )= Lim _ h 0 3(h)-0 h =3 ; f^ (1⁻ )= Lim _ h 0 [1-(1-h)]-0 -h = Lim _ h 0 h -h =-1 ]

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