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Location of Roots

The domain of...

Question

The domain of the function $y = {sin}^{- 1} (- x^{2})$ is

[- 1, 1]

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[0, 1]

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(0, 1)

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(- \infty, - 1) \cup (1, \infty)

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Solution

The correct option is A $[- 1, 1]$
$∵ - 1 \leq - x^{2} \leq 1 \Rightarrow - 1 \leq x^{2} \leq 1 \Rightarrow 0 \leq x^{2} \leq 1 (∵ x^{2} \geq 0) \Rightarrow x \in [- 1, 1]$
Hence, the domain of $y$ is $[- 1, 1] .$

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