If $f$ is an increasing function and $g$ is a decreasing function, and $fog$ is defined, then what kind of function is $fog$?

$f(x) = (20 - x^4)^{1/4}$ for $0 < x < \sqrt{5}$,then $f(f(1/2))$ is equal to

Let the functions $f: R \rightarrow R$ and $g: R \rightarrow R$ be defined as $f(x) = \begin{cases} x+2, & x < 0 \\ x^2, & x \geq 0 \end{cases}$ and $g(x) = \begin{cases} x^3, & x < 1 \\ 3x-2, & x \geq 1 \end{cases}$. Then,the number of points in $R$ where $(f \circ g)(x)$ is $NOT$ differentiable is equal to

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

If $f(x) = \frac{1}{1 - x}$,then the derivative of the composite function $f[f\{ f(x)\} ]$ is equal to

If $f: R \rightarrow R$ and $g: R \rightarrow R$ are two functions defined by $f(x)=2x-3$ and $g(x)=x^{3}+5$,then $(fog)^{-1}(x) = $