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

If $f(x) = \frac{2x - 3}{3x - 2}$ and $f_n(x) = (f \circ f \circ f \circ \dots \circ f)(x)$ ($n$ times), then $f_{32}(x) = $

Let $R$ be the set of real numbers and the mapping $f: R \rightarrow R$ and $g: R \rightarrow R$ be defined by $f(x) = 5 - x^2$ and $g(x) = 3x - 4$, then the value of $(f \circ g)(-1)$ is

Let $f(x)=x^2$ and $g(x)=\sin x$ for all $x \in R$. Then the set of all $x$ satisfying $(f \circ g \circ g \circ f)(x)=(g \circ g \circ f)(x)$,where $(f \circ g)(x)=f(g(x))$,is

If $g(x)=3x^{2}+2x-3,$ $f(0)=-3$ and $4g(f(x))=3x^{2}-32x+72,$ then $f(g(2))$ is equal to:

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