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) = $

If $g(x)=x^2+x-1$ and $(g \circ f)(x)=4 x^2-10 x+5$,then $f(2)$ is equal to

If $f: R \rightarrow R$ and $g: R \rightarrow R$ are defined by $f(x) = \begin{cases} x+2, & x>0 \\ 2-x, & x \leq 0 \end{cases}$ and $g(x) = \begin{cases} x^2-2x-2, & 1 \leq x < 2 \\ x-7, & x \geq 2 \\ x+5, & x < 1 \end{cases}$, then $\lim _{x \rightarrow 0} g(f(x))$

If $f(x)$ and $g(x)$ are two functions such that $g(x) = x - \frac{1}{x}$ and $(f \circ g)(x) = x^3 - \frac{1}{x^3}$,then $f'(1)$ is equal to:

If $f: R \rightarrow R$ and $g: R \rightarrow R$ are defined by $f(x)=x-[x]$ and $g(x)=[x]$ for $x \in R$, where $[x]$ is the greatest integer not exceeding $x$, then for every $x \in R, f(g(x))$ is equal to

If $f: R \rightarrow R$ and $g: R \rightarrow R$ are two functions defined by $f(x) = ax + b$ $(a \neq 0)$ for all $x \in R$ and $g(x) = cx^3 + d$ $(c \neq 0)$ for all $x \in R$,then $(f \circ g)^{-1}(x) =$