The domain of the real valued function $f(x) = \frac{\sqrt{6x^2+5x-6}}{\sqrt{4-x}-\sqrt{x+4}}$ is

Find the domain and range of the following real function:
$f(x) = -|x|$

The number of integral values of $\lambda$ for which the function $f(x) = \sqrt{\ln(2\lambda \cos x + 5)}$ is defined for all $x \in R$ is:

Let $f: A \rightarrow B$ be defined as $f(x) = \frac{1}{2} - \tan \left(\frac{\pi x}{2}\right)$ and $g: B \rightarrow C$ be defined as $g(x) = \sqrt{3 + 4x - 4x^2}$. If $A, B, C$ are subsets of $\mathbb{R}$ and $f$ is an onto function, then the range of the function $f(x)$ is:

Range of the function $f(x) = \frac{x^2 + x + 2}{x^2 + x + 1}; x \in R$ is

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