First slide

Functions (XII)

Question

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

Easy

A

(– ∞, 1)
B

(–1, ∞)
C

[0, 1]
D

[–1, 1]

Solution

(x) is defined if
$\begin{array}{l} 1 - \sqrt{1 - \sqrt{1 - x^{2}}} \geq 0, 1 - \sqrt{1 - x^{2}} \geq 0 and 1 - x^{2} \geq 0 \\ 1 - x^{2} \geq 0 \Rightarrow (x + 1) (x - 1) \leq 0 \Rightarrow - 1 \leq x \leq 1 \end{array}$
Clearly for these values, the other two inequalities hold.
Thus domain of f = [– 1, 1].

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