Relations and F...

Let $$f(x) =\frac {ax+b} {cx+d}$$. Then fof(x) = x provided that.

If $$f(x) =\dfrac {1}{1-x}, x \neq 0, 1$$ then the graph of the function $$y = f[f\{f(x)\}]$$ for $$x > 1 $$  is

If $$f : R\rightarrow R, f(x) = 3x-4$$, then $$f^{-1}(x)$$ is equal to

If $$f : [0, \Pi ] \rightarrow  [-1, 1]$$, f(x) = cosx, then f is.

If $$f(x) = \left\{\begin{matrix} 1&x \in Q \\ 0 &x \notin  Q\end{matrix}\right.$$ then $$fof(\sqrt 3 )$$ is equal to

If $$f : R\rightarrow R $$ and $$f(x) = x^2 - 5x + 9$$, then $$f^{-1}(9)$$ equals

If functions $$f\left ( x \right )$$ and $$g\left ( x \right )$$ are defined on $$R\rightarrow R$$ such that
$$f(x)=x+3, x$$ $$\in  $$ rational
         $$ =4x, x$$ $$\in $$ irrational
$$g(x)=x+\sqrt{5}$$, x$$\in $$ irrational
      $$  =-x, x$$ $$\in $$ rational
then $$\left ( f-g \right )\left ( x \right )$$ is

Let $$f:\left [ 1, \infty  \right )\rightarrow \left [ 3, \infty  \right )$$ & $$f\left ( x \right )=\left ( \log_{2}x \right )^{2}+2\log_{2}x+3,$$ then $$f^{-1}\left ( x \right )$$ is equal to

If $$\displaystyle f\left ( x \right )=\left ( 1-x^{3} \right )^{\frac{1}{3}}$$, then find $$fof(x)$$

Let $$\displaystyle f\left ( x \right )=\frac{3}{2}+\sqrt{x-\frac{3}{4}}$$ be a function and $$g\left ( x \right )$$ be another function such that $$g\left ( f\left ( x \right ) \right )=x,$$ then the value of $$g\left ( 20 \right )$$ will be