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) = $

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

Show that if $f: R - \{\frac{7}{5}\} \rightarrow R - \{\frac{3}{5}\}$ is defined by $f(x) = \frac{3x+4}{5x-7}$ and $g: R - \{\frac{3}{5}\} \rightarrow R - \{\frac{7}{5}\}$ is defined by $g(x) = \frac{7x+4}{5x-3}$,then $f \circ g = I_{A}$ and $g \circ f = I_{B}$,where $A = R - \{\frac{3}{5}\}$,$B = R - \{\frac{7}{5}\}$; $I_{A}(x) = x, \forall x \in A$,$I_{B}(x) = x, \forall x \in B$ are called identity functions on sets $A$ and $B$,respectively.

If $f(x) = \frac{4x + 3}{6x - 4}$, $x \neq \frac{2}{3}$ and $(f \circ f)(x) = g(x)$ where $g : R - \{\frac{2}{3}\} \to R - \{\frac{2}{3}\}$, then $(g \circ g \circ g \circ g \circ g)(3) = $

If $f(x) = \log_a x$ and $F(x) = a^x$,then $F[f(x)]$ is

If $f(x) = x^2 + 1$,then $fof(x)$ is equal to