Functions Test ...

The domain of the function, $$f(x) = \displaystyle \dfrac {1}{\sqrt{[x]^2-[x]-6}}$$  is

The domain of the function $$\ln (x-1)$$ is.

The domain of the function, $$f(x) = \log_{10} (\sqrt{x-4}+\sqrt {6-x})$$ is

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

The domain of the function $$\log \displaystyle \sqrt {\frac {3-x}{2}}$$ is.

The domain of the function $$f(x) = \displaystyle \cfrac { 1 }{ \sqrt { x-\left[ x \right]  }  } $$

The domain of the function $$\displaystyle f(x) =\frac {1}{\sqrt {(x-1) (x-2)}}$$ is.

The domain of $$f(x) = \log_e |\log_ex|$$ is.

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