First slide

Functions (XII)

Question

$The domain of f (x) = \sin^{- 1} (\frac{x^{2}}{2}) is$

Easy

A

$[- \sqrt{2}, \sqrt{2}]$
B

$(- \sqrt{2}, \sqrt{2})$
C

$(- \sqrt{2}, \sqrt{2}]$
D

$[- \sqrt{2}, \sqrt{2})$

Solution

$f (x) = \sin^{- 1} (\frac{x^{2}}{2}) is defined if$
$- 1 \leq \frac{x^{2}}{2} \leq 1 or - 2 \leq x^{2} \leq 2$
$or 0 \leq x^{2} \leq 2 (As x^{2} cannot be negative)$
$\begin{array}{l} or - \sqrt{2} \leq x \leq \sqrt{2} \\ Therefore, the domain of f (x) is [- \sqrt{2}, \sqrt{2}] . \end{array}$

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