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

If $[\cdot]$ denotes the greatest integer function,then the domain and range of the function $f(x) = \frac{\sin([x]\pi) + \tan([x]\pi)}{1 + [x]^2 + [x]^4}$ are respectively

The range of the function $f(x) = \frac{e^x \ln x \cdot 5^{(x^2 + 2)}(x^2 - 7x + 10)}{2x^2 - 11x + 12}$ 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

The range of the function $f(x) = x^2 + \frac{1}{x^2+1}$ is

If $n$ is an integer,the domain of the function $\sqrt{\sin 2x}$ is