The period of function

$f\left( x \right) = {\cos ^2}\left( {\sin x} \right) + {\sin ^2}\left( {\cos x} \right)$ is

Let $f(x) = {\cos ^{ – 1}}\left( {\frac{{2x}}{{1 + {x^2}}}} \right) + {\sin ^{ – 1}}\left( {\frac{{1 – {x^2}}}{{1 + {x^2}}}} \right)$ then the value of $f(1) + f(2)$, is –

If the graph of non-constant function is symmetric about the point $(3,4)$ , then the value of $\sum\limits_{r = 0}^6 {f(r) + f(3)} $ is equal to

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

Suppose $f(x) = {(x + 1)^2}$ for $x \ge – 1$. If $g(x)$ is the function whose graph is the reflection of the graph of $f(x)$ with respect to the line $y = x$, then $g(x)$ equals