The domain of the function $y=f(x)$,where $x$ and $y$ are related by $2^x+2^y=2$ is

The least value of $2^{(x^2 - 3)^3+27}$ is-

If the domain of the function $\log _5(18 x-x^2-77)$ is $(\alpha, \beta)$ and the domain of the function $\log _{(x-1)}\left(\frac{2 x^2+3 x-2}{x^2-3 x-4}\right)$ is $(\gamma, \delta)$,then $\alpha^2+\beta^2+\gamma^2$ is equal to :

The domain of the function $f(x) = \frac{1}{\sqrt{[x]^2 - 3[x] - 10}}$ is (where $[x]$ denotes the greatest integer less than or equal to $x$).

If $A \subseteq Z$ and the function $f: A \rightarrow R$ is defined by $f(x) = \frac{1}{\sqrt{64 - (0.5)^{24 + x - x^2}}}$,then the sum of all absolute values of elements of $A$ is

If the range of the function $f(x) = -3x - 3$ is $\{3, -6, -9, -18\}$, then which of the following elements is not in the domain of $f$?