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

If $t$ is a parameter, $A=(a \sec t, b \tan t)$, $B=(-a \tan t, b \sec t)$ and $O=(0,0)$, then the locus of the centroid of $\triangle O A B$ is

If $f:[2, \infty) \rightarrow R$ is defined by $f(x)=x^2-4 x+5$, then the range of $f$ is

If $f(x)=-|x|$, then $($ fofof $)(x)+($ fofof $)(-x)=$