First slide

Functions (XII)

Question

The domain of f(x) $= \sin^{- 1} [x] (where [ ] represents the greatest integer function).$

Moderate

A

$[- 1, 2)$
B

$(- 1, 2)$
C

$[- 1, 2]$
D

$[1, 2]$

Solution

$f (x) = \sin^{- 1} [x] is defined if$
$\begin{array}{ll} - 1 \leq [x] \leq 1 \\ or [x] = - 1, 0, 1 \\ or x \in [- 1, 2) \end{array}$
$So, range is \{\sin^{- 1} (- 1), \sin^{- 1} 0, \sin^{- 1} 1\} \equiv {- \frac{π}{2}, 0, \frac{π}{2}}$

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