The domain of definition of the function $y(x)$ given by $2^x + 2^y = 2$ is

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

The domain of the function $f(x) = \frac{\cos^{-1}\left(\frac{x^{2}-5x+6}{x^{2}-9}\right)}{\log_{e}(x^{2}-3x+2)}$ is:

The domain of the real-valued function $f(x) = \sqrt{\frac{2x^2 - 7x + 5}{3x^2 - 5x - 2}}$ is

The domain of the function $f(x) = \sqrt{\frac{x}{1+x}}$ is

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