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

Question

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, continuous for every real x, discontinuous only at x = 0, discontinuous only at integral values of x, continuous only at x = 0

MARKS App · Accepted Answer

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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