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

Question

Find the domain of the following function:

$\text{f(x)}=\sin^{-1}\sqrt{\text{x}^2-1}$

✓

Answer

To the domain of sin^-1y which is [-1, 1]

$\therefore$ x² -1 $\in$ [0, 1] as square root can not be negative

⇒ x²$\in$ [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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