The domain of $f(x) = \log \left[(2.5)^{3-x^2} - (0.4)^{x+9}\right]$ is

If $f: R \rightarrow R$ is defined by $f(x)=[2x]-2[x]$ for $x \in R$,then the range of $f$ is (Here $[x]$ denotes the greatest integer not exceeding $x$)

Domain of function $f(x) = \log|5\{x\} - 2x|$ is $x \in R - A$,then $n(A)$ is (where $\{.\}$ denotes fractional part function)

If $D \subseteq R$ and $f: D \rightarrow R$ defined by $f(x) = \frac{x^2+x+a}{x^2-x+a}$ is a surjection, then '$a$' lies in the interval

The range of $f(x) = [\cos x + \sin x]$ is (Where $[.]$ is $G.I.F.$)

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