Let $f (x) = [c o s x + s i n x], 0 < x < 2 π,$ where [x] denotes the greatest integer less than of equal to x. The number of points of discontinuity of f(x) is

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Solution

The correct option is B 5
$[c o s x + s i n x] = [\sqrt{2} c o s (x - \frac{π}{4})]$
We know that [x] is discontinuous at integral values of x,
Now, $\sqrt{2} c o s (x - \frac{π}{4})$ is an integer.
$\Rightarrow x = \frac{π}{2}, \frac{3 π}{4}, π, \frac{3 π}{2}, \frac{7 π}{4}$ .

The function is discontinuous at 5 points in its domain

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