If $f: R \rightarrow A$ defined by $f(x) = \frac{1}{x^2+2x+2}$,$\forall x \in R$ is surjective,then $A =$

If $f: A \rightarrow B$ is an onto function such that $f(x)=\sqrt{|x|-x}+\frac{1}{\sqrt{|x|-x}}$,then $A$ and $B$ are respectively.

Is it true that $x = e^{\log x}$ for all real $x$?

Find the set $\{x \in R : \frac{\sqrt{|x|^2-2|x|-8}}{\log(2-x-x^2)} \text{ is a real number}\}$.

If $e^x + e^{f(x)} = e$, then the domain of $f(x)$ is

Let $\rho$ be a relation defined on the set of natural numbers $N$, as $\rho = \{(x, y) \in N \times N: 2x + y = 41\}$. Then the domain $A$ and range $B$ are: