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The domain of the function $f (x) = \sqrt{1 - \sqrt{1 - \sqrt{1 - x^{2}}}} is$

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(– ∞, 1)

(–1, ∞)

[0, 1]

[–1, 1]

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detailed solution

Correct option is D

(x) is defined if 1−1−1−x2≥0,1−1−x2≥0 and 1−x2≥01−x2≥0⇒(x+1)(x−1)≤0⇒−1≤x≤1Clearly for these values, the other two inequalities hold.Thus domain of f = [– 1, 1].

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The domain of the function f(x)=1−1−1−x2 is

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The domain of the function $f (x) = \sqrt{1 - \sqrt{1 - \sqrt{1 - x^{2}}}} is$