First slide

Continuity

Question

If [.] denotes the greatest integer function then the number of points where $f (x) = [x] + [x + \frac{1}{3}] + [x + \frac{2}{3}]$ is discontinuous for $x \in (0, 3)$ are

Moderate

A

2
B

9
C

8
D

10

Solution

$f (x) = [3 x] is discontinuous when 3 x = an integer$
$\Rightarrow x = \frac{1}{3}, \frac{2}{3}, \frac{3}{3}, \frac{4}{3}, \frac{5}{3}, \frac{6}{3}, \frac{7}{3}, \frac{8}{3} \in (0, 3)$

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