First slide

Functions (XII)

Question

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

Moderate

A

$[0, 1]$
B

$[- 1, 1]$
C

$[- \infty, \infty]$
D

$(- 1, 1)$

Solution

$1 - x^{2} \geq 0 \Rightarrow (x - 1) (x + 1) ⩽ 0 \Rightarrow x \in [- 1, 1]$

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