If the function $f: R \rightarrow R$ is defined by $f(x) = (x^{2} + 1)^{35}, \forall x \in R,$ then $f$ is

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

Let $R$ be the set of all real numbers. Statement $I$: The function $f: \left(-\frac{\pi}{2}, \frac{\pi}{2}\right) \rightarrow R$ defined by $f(x) = \sec x + \tan x$ is a one-one function. Statement $II$: The function $f: [0, \infty) \rightarrow R$ defined by $f(x) = x^2$ is a one-one function. Which of the above statements is(are) true?

If $f: R \rightarrow C$ is defined by $f(x)=e^{2 i x}$ for $x \in R$,then $f$ is (where $C$ denotes the set of all complex numbers)

Let $N$ be the set of all natural numbers,$Z$ be the set of all integers and $\sigma: N \rightarrow Z$ be defined by $\sigma(n)=\begin{cases} \frac{n}{2}, & \text{if } n \text{ is even} \\ -\frac{n-1}{2}, & \text{if } n \text{ is odd} \end{cases}$. Then,

The function $f: C \rightarrow C$ defined by $f(x) = \frac{ax + b}{cx + d}$ for $x \in C$, where $bd \neq 0$, reduces to a constant function if: