If $n(A) = 5$ and $n(B) = 8$,how many possible functions can be defined from $A$ to $B$?

If the function $f: R \rightarrow R$ is defined by $f(x) = |x|(x - \sin x)$,then which of the following statements is $TRUE$?

Let $g: N \rightarrow N$ be defined as
$g(3n+1)=3n+2$
$g(3n+2)=3n+3$
$g(3n+3)=3n+1, \text{ for all } n \geq 0$
Then which of the following statements is true?

Let $X$ be a set with exactly $5$ elements and $Y$ be a set with exactly $7$ elements. If $\alpha$ is the number of one-one functions from $X$ to $Y$ and $\beta$ is the number of onto functions from $Y$ to $X$,then the value of $\frac{1}{5!}(\beta-\alpha)$ is.

Check the injectivity and surjectivity of the following function $f : N \rightarrow N$ given by $f(x) = x^{3}$.

Let $A \subseteq R, B \subseteq R$ and $f: A \rightarrow B$ be defined by $f(x)=x^2-3x+2$. If $f$ is a bijection,then