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  4. The domain of the function y= sin -1(-x2) is

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Q. The domain of the function $y=\sin ^{-1}\left(-x^2\right)$ is

Inverse Trigonometric Functions

Solution:

Given, $y=\sin ^{-1}\left(-x^2\right)$
$\Rightarrow \sin y=-x^2$
We know that, $-1 \leq \sin y \leq 1$
$\Rightarrow -1 \leq-x^2 \leq 1 \Rightarrow -1 \leq x^2 \leq 1$
$\Rightarrow 0 \leq x^2 \leq 1 \Rightarrow| x \mid \leq 1 $
$\Rightarrow -1 \leq x \leq 1$