The domain of the function defined by f ( x ) = sin - 1 ( x ? 1 ) is:

Question

The domain of the function defined by $f (x) = \sin^{- 1} \sqrt{(x - 1)}$ is:

Smart Achievers · Accepted Answer

(1)

Ans: [1, 2]

Explanation:

We know that $\sin^{- 1} x$ is defined for

$x \in [- 1, 1]$

$∴$ $f (x) = \sin^{- 1} \sqrt{x - 1} is defined if$

$\Rightarrow$ $0 \leq \sqrt{x - 1} \leq 1$

$[∵ \sqrt{x - 1} \geq 0 and - 1 \leq \sqrt{x - 1} \leq 1]$

$\Rightarrow 0 \leq x - 1 \leq 1$

$\Rightarrow 1 \leq x \leq 2$

$∴$ $x \in [1, 2]$

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