For the greatest integer function $f(x) = [x]$,where $x \in R$,which of the following is true?

The function $f(x) = \sin (\log (x + \sqrt {x^2 + 1}))$ is

If a function $f: R-\{l\} \to R-\{m\}$ defined by $f(x) = \frac{x+3}{x-2}$ is a bijection,then $3l - 2m =$

Let $x$ denote the total number of one-one functions from a set $A$ with $3$ elements to a set $B$ with $5$ elements,and $y$ denote the total number of one-one functions from the set $A$ to the set $A \times B$. Then ...... .

For real $x,$ let $f(x) = x^3 + 5x + 1,$ then

Let $A=\{1,2,3\}, \,B=\{4,5,6,7\}$ and let $f=\{(1,4),\,(2,5),\,(3,6)\}$ be a function from $A$ to $B$. Show that $f$ is one-one.