Domain of the real valued function $f(x) = \frac{x+2}{9-x^{2}}$ is

The set of values of $\alpha$ such that $f: R \rightarrow [0, \frac{\pi}{2})$ defined by $f(x) = \tan^{-1}(x^2 + x + \alpha^2)$ is onto 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 $A =$

If the domain of the function $f(x) = \log_e \left( \frac{2x+3}{4x^2+x-3} \right) + \cos^{-1} \left( \frac{2x-1}{x+2} \right)$ is $(\alpha, \beta]$,then the value of $5\beta - 4\alpha$ is equal to

The range of the function $f(x) = \sqrt{9 - x^2}$ is

The domain of the real valued function $f(x) = \sqrt{\cos (\sin x)} + \cos^{-1} \left( \frac{1 + x^2}{2 x} \right)$ is