Let $A = \{x \in R, x \neq 0, -4 \leq x \leq 4\}$ and $f: A \rightarrow R$ be defined by $f(x) = \frac{|x|}{x}$ for $x \in A$. Then, the range of $f$ is

The mid-point of the domain of the function $f(x) = \sqrt{4 - \sqrt{2x + 5}}$ for real $x$ is

Find the range of the function $f(x)$ defined by:
$f(x) = \begin{cases} 2x-3, & x < -1 \\ 1-x^2, & -1 \leq x \leq 1 \\ 3x^2+2, & x > 1 \end{cases}$

Let $D$ be the domain of the function $f(x) = \sin^{-1} \left(\log_{3x} \left(\frac{6+2 \log_3 x}{-5x}\right)\right)$. If the range of the function $g: D \rightarrow R$ defined by $g(x) = x - [x]$ (where $[x]$ is the greatest integer function) is $(\alpha, \beta)$,then $\alpha^2 + \frac{5}{\beta}$ is equal to

The domain of the function $f(x) = \log |\log x|$ is:

If $[x]$ represents the greatest integer function, then the set of all real values of $x$ for which $f(x)=\sqrt{\frac{[x]-x}{x-[x]}}$ is real is