If $f: N \rightarrow R$ is defined by $f(1)=-1$ and $f(n+1)=3f(n)+2$ for $n \geq 1$, then $f$ is

If $f: R \rightarrow R$ is defined by $f(x) = x^2 + 3x + 4$,then the function $f$ is . . . . . . .

Show that a one-one function $f: \{1, 2, 3\} \rightarrow \{1, 2, 3\}$ must be onto.

The number of one-one functions from the set $A = \{1, 2, 3, 4, 5\}$ to itself is . . . . . . .

If $f: R \rightarrow R$ is defined by $f(x) = \begin{cases} 2x & : x > 3 \\ x^2 & : 1 < x \leq 3 \\ 3x & : x \leq 1 \end{cases}$,then the value of $f(-1) + f(2) + f(4)$ is:

Prove that the Greatest Integer Function $f: R \rightarrow R$,given by $f(x)=[x]$,is neither one-one nor onto,where $[x]$ denotes the greatest integer less than or equal to $x$.