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Relations and Functions — MATHS STD 10 — Question

Tamilnadu BoardEnglish MediumSTD 10MATHSRelations and Functions2 Marks
Question
Find the domain of the function $f(x)=\sqrt{1+\sqrt{1-\sqrt{1-x^2}}}$
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Answer

$f(x)=\sqrt{1+\sqrt{1-\sqrt{1-x^2}}} $
$ \sqrt{1-x^2}=\sqrt{(1+x)(1-x)} $
$ \Rightarrow x=-1 \text { or } x=1 $
$ =-1 \leq x \leq 1 $
$ \text { Domain of } f(x)=\{-1,0,1\}$

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