Range of the function $f(x) = {\sin ^2}({x^4}) + {\cos ^2}({x^4})$ is

If $f(x) = \sin \log x$, then the value of $f(xy) + f\left( {\frac{x}{y}} \right) – 2f(x).\cos \log y$ is equal to

For $x\,\, \in \,R\,,x\, \ne \,0,$ let ${f_0}(x) = \frac{1}{{1 – x}}$ and ${f_{n + 1}}(x) = {f_0}({f_n}(x)),$ $n\, = 0,1,2,….$  Then the value of ${f_{100}}(3) + {f_1}\left( {\frac{2}{3}} \right) + {f_2}\left( {\frac{3}{2}} \right)$ is equal to

If the domain of the function $f(x)=\log _e\left(4 x^2+11 x+6\right)+\sin ^{-1}$ $(4 x+3)+\cos ^{-1}\left(\frac{10 x+6}{3}\right) \text { is }(\alpha, \beta]$ Then $36|\alpha+\beta|$ is equal to :

If $f(x) = \frac{{{x^2} – 1}}{{{x^2} + 1}}$, for every real numbers. then the minimum value of $f$