Question

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

Answer 1

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

We know that the expression inside root should always be $>0$

Therefore, $1-x^2\ge 0$

$\Rightarrow x^2-1\le 0$

$\Rightarrow (x-1)(x+1)\le 0$

$\Rightarrow -1\le x\le 1$

Therefore, domain of $f\left(x\right)is[-1,1]$