Question

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

(a) $[1,2]$ (b) $[-1,1]$ (c) $[0,1]$ (d) None of these

Answer 1

(a) $\because f\left(x\right)=si{n}^{-1}\sqrt{x-1}\Rightarrow 0\le x-1\le 1[\because \sqrt{x-1}\ge 0and-1\le \sqrt{x-1}\le 1]\Rightarrow 1\le x\le 2\Rightarrow x\in [1,2]$