First slide

Functions (XII)

Question

Find the range of f(x) $f (x) = \sin^{- 1} [x]$

Easy

A

$\{- \frac{π}{2}, 0\}$
B

$\{- \frac{π}{2}, 0, \frac{π}{2}\}$
C

$\{- \frac{π}{2}, \frac{π}{2}\}$
D

$ϕ$

Solution

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

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