Find the domain of
\[
p(x)=\sin^{-1}(1-2x^2).
\]
Hence, find the value(s) of \(x\) for which
\[
p(x)=\frac{\pi}{6}.
\]
Also, write the range of
\[
2p(x)+\frac{\pi}{2}.
\]
Show Hint
When solving equations involving \(x^2\), never forget to include the negative square root. Dropping the \(\pm\) sign will cause you to miss half of the valid solutions!