Question

Find domain of $\sin ^{-1}\left(2 x^2-1\right)$

Answer 1

SOLUTION : Let $y=\sin ^{-1}\left(2 x^2-1\right)$

For $y$ to be defined $-1 \leq\left(2 x^2-1\right) \leq 1 \Rightarrow 0 \leq 2 x^2 \leq 2 \Rightarrow 0 \leq x^2 \leq 1 \Rightarrow x \in[-1,1]$.