Q22 / 54 · JEE Advanced 2017 (Paper 1) · Mathematics

Let $[x]$ be the greatest integer less than or equals to $x$ . Then, at which of the following point(s) the function $f (x) = x \cos (π (x + [x]))$ is discontinuous?

Solution

$f (x) = x \cos (π x + [x] π)$

$\Rightarrow f (x) = {(- 1)}^{[x]} x \cos (π x)$

$[x]$ is discontinuous at all integers and $x \cos π x$ is continuous everywhere.

At $x = 0$ , $f (x) = 0$ , so it's continuous.

At other integral points, $f (x)$ is discontinuous.

Hence, the correct answer is options: 'A', 'B', 'D'.