Let $f : R \to R$ be a function defined by $f(x) =  - \frac{{|x{|^3} + |x|}}{{1 + {x^2}}}$; then the graph of $f(x)$ is lies in the :-

Let $f(\theta)$ is distance of the line $( \sqrt {\sin \theta } )x + (  \sqrt {\cos  \theta })y +1 = 0$ from origin. Then the range of $f(\theta)$ is -

The minimum value of the function $f(x) = {x^{10}} + {x^2} + \frac{1}{{{x^{12}}}} + \frac{1}{{\left( {1\ +\ {{\sec }^{ - 1}}\ x} \right)}}$ is

If a function $f(x)$ is such that $f\left( {x + \frac{1}{x}} \right) = {x^2} + \frac{1}{{{x^2}}};$ then  $(fof )$ $\sqrt {11} )$ =

If function $f(x) = \frac{1}{2} - \tan \left( {\frac{{\pi x}}{2}} \right)$; $( - 1 < x < 1)$ and $g(x) = \sqrt {3 + 4x - 4{x^2}} $, then the domain of $gof$ is

The range of the function $f(x) = \frac{x}{{1 + \left| x \right|}},\,x \in R,$ is