Find the number of all one-one functions from set $A = \{1, 2, 3\}$ to itself.

$A$ function $f: R \rightarrow R$ defined by $f(x) = \begin{cases} 2x+3, & x \leq \frac{4}{3} \\ -3x^2+8x, & x > \frac{4}{3} \end{cases}$ is

Let $f: R \rightarrow R$ be defined by $f(x)=x^{4}$,then

The function $f:R \to R$ defined by $f(x) = (x - 1)(x - 2)(x - 3)$ is

Show that the function $f : R \rightarrow R$ given by $f(x) = x^{3}$ is injective.

Consider the identity function $I_{N}: N \rightarrow N$ defined as $I_{N}(x) = x$ for all $x \in N$. Show that although $I_{N}$ is onto,the function $I_{N} + I_{N}: N \rightarrow N$ defined as $(I_{N} + I_{N})(x) = I_{N}(x) + I_{N}(x) = x + x = 2x$ is not onto.