Question

The domain of the function \(f(x) = \sqrt {1 - \sqrt {1 - \sqrt {1 - {x^2}} } } \) is:
1. {x | x < 1}
2. {x | x > -1}
3. [0, 1]
4. [-1, 1]

Answer 1

Correct Answer - Option 4 : [-1, 1]

Given,

\(f(x) = \sqrt {1 - \sqrt {1 - \sqrt {1 - {x^2}} } } \)

Here, 1 - x² ≥ 0

⇒ x² - 1 ≤ 0

⇒ (x - 1) (x + 1) ≤ 0

when, x - 1 = 0 ⇒ x = 1

when, x + 1 = 0 ⇒ x = -1

thus, domain of x = [-1, 1]