Question

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

• A. $[1,2]$
• B. $[0,2]$
• C. $[0,1]$
• D. $noneofthese$

Answer 1

The correct option is A $[1,2]$

For the square root to be defined:
$x-1\ge 0⟹x\ge 1$ (1)
For inverse sine to be defined,
$-1\le \sqrt{x-1}\le 1$
As square is always non-negative:
$0\le \sqrt{x-1}\le 1$
$⟹0\le x-1\le 1$
$⟹1\le x\le 2$ (2)
Intersection of the two intervals (1) and (2) gives:
$x\in [1,2]$