Explanation

(c)
Given, $f(x) = \frac{\sqrt{4 - x^{2}}}{\sin^{- 1}{(2 - x)}}$
For $f(x)$ to be defined $4 - x^{2} \geq 0;\ - 1 \leq 2 - x \leq$ and $2 - x \neq 0$
$\Rightarrow \ - 2 \leq x \leq 2$; $1 \leq x \leq 3$ and $x \neq 2$
$\therefore$ Domian of $f(x)$ is $\lbrack 1,\ 2)$.