Prove that the function $f: R \rightarrow R$, given by $f(x)=2 x,$ is one-one and onto.

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

Let $X$ be a non-empty set and let $P(X)$ denote the collection of all subsets of $X$. Define $f: X \times P(X) \rightarrow R$ by $f(x, A)=\left\{\begin{array}{ll}1, & \text { if } x \in A \\ 0, & \text { if } x \notin A^*\end{array}\right.$ Then, $f(x, A \cup B)$ equals

If $y = f(x) = \frac{{ax + b}}{{cx – a}}$, then $x$ is equal to

Range of $f(x) = \;[x]\; – x$ is