First slide

Functions (XII)

Question

$The number of elements in the domain of the function$ $f (x) = \sin^{- 1} (\frac{x^{2} - 2 x}{3}) + \sqrt{[x] + [- x]}, (where [.] denotes$ $the greatest integer function) is equal to$

Moderate

A

6
B

4
C

3
D

5

Solution

$f (x) = \sin^{- 1} (\frac{x^{2} - 2 x}{3}) + \sqrt{[x] + [- x]}$
$\sin^{- 1} (\frac{x^{2} - 2 x}{3}) is defined for - 1 \leq \frac{x^{2} - 2 x}{3} \leq 1$
$and \sqrt{[x] - [- x]} is defined only for integral values of x$
$\Rightarrow x = - 1, 0, 1, 2, 3$

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