The domain of definition of f(x) = sin^-1(-x^2), is

The domain of $sin^{-1} x $ is [-1,1]. Therefore, $f(x)= sin^{-1}(-x^2)$ is defined for all x satisfting

$-1 ≤ -x^2 ≤ 1$

$⇒ 1 ≥ x^2 ≥ -1 ⇒ 0 ≤ x^2 ≤ 1$,

$x^2 ≤1 ⇒x^2 - 1 ≤ 0$

$⇒ (x-1)(x+1) ≤ 0 ⇒ -1 ≤x ≤ 1 $

Hence, the domain of $f(x) = sin^{-1}(-x^2) $ is [-1,1]