Let $A=\left\{x\in R:-1\le x\le 1\right\}$ and $f:A\to A$ be a mapping defined by $f\left(x\right)=x\left|x\right|$. Then $f$ is

Let $f\left(x\right)=\sin x+\cos ax$ be a periodic function. Then,

Let $f:X\to Y$ and $A, B$ are non-void subsets of $Y,$ then (where the symbols have their usual interpretation)

If $f:S\to R,$ where $S$ is the set of all non-singular matrices of order $2$ over $R$ and $f\left[\left(\begin{array}{ll}a& b\\ c& d\end{array}\right)\right]=ad-bc,$ then