The range of the real valued function $f(x) = \frac{1}{x - |x|}$ is

Let the domains of the functions $f(x) = \log_4 \log_3 \log_7(8 - \log_2(x^2 + 4x + 5))$ and $g(x) = \sin^{-1}(\frac{7x + 10}{x - 2})$ be $(\alpha, \beta)$ and $[\gamma, \delta]$,respectively. Then $\alpha^2 + \beta^2 + \gamma^2 + \delta^2$ is equal to:

Let $f: R - \{2, 6\} \rightarrow R$ be a real-valued function defined as $f(x) = \frac{x^2+2x+1}{x^2-8x+12}$. Then the range of $f$ is

Let $y = \sqrt{\frac{(x + 1)(x - 3)}{(x - 2)}}$. Then,the set of all real values of $x$ for which $y$ takes real values is:

Let $f:[2, \infty) \rightarrow R$ be the function defined by $f(x)=x^{2}-4x+5$. Then the range of $f$ is:

If the domain of the greatest integer function is the set of real numbers,then the range will be the set of