Domain of $f(x) = (x^2 - 1)^{-1/2}$ is

The domain of the real valued function $f(x) = \log_2 \log_3 \log_5(x^2 - 5x + 11)$ is

Let $[x]$ denote the greatest integer $\leq x$,where $x \in \mathbb{R}$. If the domain of the real-valued function $f(x) = \sqrt{\frac{|[x]|-2}{|[x]|-3}}$ is $(-\infty, a) \cup [b, c) \cup [4, \infty)$,where $a < b < c$,then the value of $a+b+c$ is:

If $f:[2, \infty) \rightarrow R$ is defined by $f(x)=x^2-4x+5$,then the range of $f$ is

If $f: R \rightarrow A$ defined by $f(x) = \frac{1}{x^2+2x+2}$,$\forall x \in R$ is surjective,then $A =$

The domain of $f(x) = \sqrt{\left(\frac{1}{\sqrt{x}} - \sqrt{x+1}\right)}$ is