Question

The range of the function f(x) = sin [x], $-\frac{\pi }{4}\le x\le \frac{\pi }{4}$ where [x] denotes the greatest integer, is

• A. {0}
• B. {0, -1}
• C. {0, $\pm$ sin 1}
• D. {0, - sin 1}

Answer 1

The correct option is D {0, - sin 1}

$-\frac{\pi }{4}\le x<0$ or $0\le x\le \frac{\pi }{4}$
$\Rightarrow$ [x] = -1 or [x] = 0
$\Rightarrow$ sin [x] = sin (-1) or sin 0
$\Rightarrow$ sin [x] = - sin 1 or 0
$\therefore$ R (f) = {-sin 1, 0}