$f$ is a real valued function satisfying the relation $f\left(3 x+\frac{1}{2 x}\right)=9 x^2+\frac{1}{4 x^2}$. If $f\left(x+\frac{1}{x}\right)=1$, then $x$ is equal to

If $f(x)=\frac{2 x-3}{3 x-2}$ and $f_n(x)=($ fofofo .......n times) $(x)$, then $f_{32}(x)=$

The domain of the real valued function $f(x)=\sqrt{\cos (\sin x)}+\cos ^{-1}\left(\frac{1+x^2}{2 x}\right)$ is

The domain of the function $f(x)=\sin ^{-1}\left(\log _2\left(\frac{x^2}{2}\right)\right)$ is