Domain of f(x)= ^ -1 (-x^2 ) is : - Vidyadip

Question

Domain of $f(x)=\sin ^{-1}\left(-x^2\right)$ is :

✓

Answer

(C)
$f(x)=\sin ^{-1}(-x)^2$ will be defined if $-1 \leq-x^2 \leq 1$$
\begin{array}{ll}
\Rightarrow & 1 \geq x^2 \geq-1 \\
\Rightarrow & 0 \leq x^2 \leq 1 \\
\Rightarrow & x^2-1 \leq 0
\end{array}
$
$
\begin{array}{ll}
\Rightarrow & -1 \leq x \leq 1 \\
\Rightarrow & x \in[-1,1]
\end{array}
$
Hence function $f(x)=\sin ^{-1}\left(-x^2\right)$ has domain $[-1,1]$
Hence correct option is (C)

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