If $f(x) = \frac{1 - x}{1 + x},$ then $f[f(\cos 2\theta)] = $

If $f$ is an exponential function and $g$ is a logarithmic function,then $fog(1)$ will be

$f: R - \left(-\frac{3}{5}\right) \rightarrow R$ is defined by $f(x) = \frac{3x-2}{5x+3}$,then $f \circ f(1)$ is

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 $f: A \rightarrow B$ and $g: B \rightarrow C$ are functions such that $g \circ f: A \rightarrow C$ is onto,then a necessary condition is:

If $f(x) = \frac{3x+4}{5x-7}, x \neq \frac{7}{5}$ and $g(x) = \frac{7x+4}{5x-3}, x \neq \frac{3}{5}$,then $(g \circ f)(3) = $