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

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

Let $f: R \rightarrow R$ be the Signum Function defined as $f(x) = \begin{cases} 1, & x > 0 \\ 0, & x = 0 \\ -1, & x < 0 \end{cases}$ and $g: R \rightarrow R$ be the Greatest Integer Function given by $g(x) = [x]$,where $[x]$ is the greatest integer less than or equal to $x$. Do $fog$ and $gof$ coincide in $(0, 1]$?

If $f(x) = \frac{(\tan 1^{\circ}) x + \log_{e}(123)}{x \log_{e}(1234) - (\tan 1^{\circ})}$,$x > 0$,then the least value of $f(f(x)) + f(f(4/x))$ is $...........$.

If $f(x) = \frac{x}{\sqrt{1 + x^2}}$,then $(fofof)(x) = $

Let $S, T, U$ be three non-void sets and $f: S \rightarrow T, g: T \rightarrow U$ be functions such that $g \circ f: S \rightarrow U$ is surjective. Then,