Question

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

• A. $(\infty ,1)$
• B. $(1,\infty )$
• C. $[0,1]$
• D. $[-1,1]$

Answer 1

The correct option is D $[-1,1]$

For given function to be defined,

$(1-x^2)>0\Rightarrow x^2-1\le 0\Rightarrow x\in [-1,1]$