If a function $f: R \rightarrow R$ is defined by $f(x)=x^3-x$,then $f$ is

The set $A$ has $4$ elements and the set $B$ has $5$ elements. Then,the number of injective mappings that can be defined from $A$ to $B$ is:

If $f : R \rightarrow R$ such that $f(x) = 5x - 3\cos x - 4\sin x$,then the function $f(x)$ is

Check the injectivity and surjectivity of the following function $f: N \rightarrow N$ defined by $f(x)=x^{2}$.

Let $f: N \rightarrow N$ be defined by $f(n) = \begin{cases} \frac{n+1}{2}; & \text{if } n \text{ is odd} \\ \frac{n}{2}; & \text{if } n \text{ is even} \end{cases}$,for all $n \in N$ then $f$ is $\dots \dots \dots$

Let $A = \{1, 2, 3, \ldots, 7\}$ and let $P(A)$ denote the power set of $A$. If the number of functions $f: A \rightarrow P(A)$ such that $a \in f(a)$ for all $a \in A$ is $m^n$,where $m, n \in N$ and $m$ is the least possible value,then $m + n$ is equal to . . . . . . .