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The domain of definition of $f(x) = sin^{-1}(-x^2)$, is |
[-1,1] [0,1] [-1,0] [-2,2] |
[-1,1] |
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] |
