If $R$ is the set of all real numbers and $f: R-\{2\} \rightarrow R$ is defined by $f(x)=\frac{2+x}{2-x}$ for $x \in R-\{2\}$, find the range of $f(x)$.

The domain of the function $f(x) = \sqrt{x - x^2} + \sqrt{4 + x} + \sqrt{4 - x}$ is

$A$ and $B$ are subsets of $R$. Every element $x$ of $A$ is mapped to an element of $B$ by the rule, $y(x) = \begin{cases} \frac{5x}{(x-3)(x+3)} & \text{if } x \neq -1 \\ -1 & \text{if } x = -1 \end{cases}$, then $A =$

The domain of the function $f: R \rightarrow R$ defined by $f(x) = \sqrt{x^{2}-7x+12}$ is

Define a function $f(x) = \frac{16x^2 - 96x + 153}{x - 3}$ for all real $x \neq 3$. The least positive value of $f(x)$ is

The domain of $f(x) = \frac{\log_{(x+1)}(x-2)}{x^2 - (2x + 3)}$ for $x \in R$ is