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If f : R → R is a function defined by f ( x ) = x s i n 2 x - 1 2 π , where x denotes the greatest integer function, then f is

Options

  1. Acontinuous for every real x
  2. Bdiscontinuous only at x = 0
  3. Cdiscontinuous only at integral values of x
  4. Dcontinuous only at x = 0

Correct answer

C. discontinuous only at integral values of x

Step-by-step solution

Doubtful points are x = n ,   ∀ n ∈ Ι L . H . L = l i m x → n - x s i n 2 x - 1 2 π = n - 1 s i n 2 n - 1 2 π = ± n - 1 R . H . L = l i m x → n + x s i n 2 x - 1 2 π = n s i n 2 n - 1 2 π = ± n f n = ± n Clearly, LHL , RHL , f n all cannot be equal for any n ∈ Ι Hence, discontinuous at all integeral values of x

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