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

If $f: R \rightarrow R$ is defined by $f(x) = x + 2|x + 1| + 2|x - 1|$,then the element in the co-domain,which has a unique pre-image in the domain is

$A$ function $f$ from the set of natural numbers $\mathbb{N}$ to the set of integers $\mathbb{Z}$ is defined by $f(n) = \begin{cases} \frac{n-1}{2}, & \text{if } n \text{ is odd} \\ -\frac{n}{2}, & \text{if } n \text{ is even} \end{cases}$. The function $f$ is:

$A$ function from $A = \{x : -1 \leq x \leq 1\}$ to itself which is not a bijection is

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 ...... .

If $R$ denotes the set of all real numbers,then the function $f: R \rightarrow R$ defined by $f(x)=|x|$ is