Find the domain of the following function:f(x)= ^ -1 x^2-1 - Vidyadip

Question

Find the domain of the following function:$\text{f(x)}=\sin^{-1}\sqrt{\text{x}^2-1}$

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Answer

To the domain of $sin^{-1}y$ which is [-1, 1] $\therefore x^2 -1 \in$ [0, 1] as square root can not be negative
$\Rightarrow x^2 \in [1, 2]$
$\Rightarrow\text{x}\in\big[-\sqrt2,-1\big]\cup\big[1,\sqrt2\big]$
Hence, the domain is $\big[-\sqrt2,-1\big]\cup\big[1,\sqrt2\big]$

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