If f(x) = [sin x] + [cos x], $x \in [0, 2 π]$ , where [.] denotes the greatest integer function. Then, the total number of points, where f(x) is non – differentiable, is

Q. Let

f (x) = [3 + 2 cos x], x \in (- \frac{π}{2}, \frac{π}{2})

, where [.] denotes the greatest integer function. The number of points of discontinuity of

f (x)

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Let f(x)=[x3−3], where [.] denotes the greatest integer function. Then the number of points in the interval (1,2) where the function is discontinuous, is

The correct option is C 6f(x)=[x3−3], x∈(1,2) For x∈(1,2), x3−3∈(−2,5) We know that [x] is discontinuous whenever x is an integer. ∴f(x)=[x3−3] is discontinuous at all integral points in its range i.e., at six points, corresponding to x3−3∈{−1,0,1,2,3,4}

Let $f (x) = [x^{3} - 3],$ where $[.]$ denotes the greatest integer function. Then the number of points in the interval $(1, 2)$ where the function is discontinuous, is