The range of $f(x)=4 \sin ^{-1}\left(\frac{x^2}{x^2+1}\right)$ is
$[0, \pi]$
$[0,2 \pi)$
$[0, \pi)$
$[0,2 \pi]$
If $f\left( x \right) + 2f\left( {\frac{1}{x}} \right) = 3x,x \ne 0$ and $S = \left\{ {x \in R:f\left( x \right) = f\left( { - x} \right)} \right\}$;then $S :$
The range of the function $f(x) = \frac{x}{{1 + \left| x \right|}},\,x \in R,$ is
The mid-point of the domain of the function $f(x)=\sqrt{4-\sqrt{2 x+5}}$ real $x$ 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
The range of $f(x) = \cos (x/3)$ is