If $f: Z \rightarrow Z$,$f(x) = \begin{cases} \frac{x}{2}, & \text{if } x \text{ is even} \\ 0, & \text{if } x \text{ is odd} \end{cases}$,then $f$ is

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

Let the functions $f$ and $g$ be $f: [0, \frac{\pi}{2}] \rightarrow R$ given by $f(x) = \sin x$ and $g: [0, \frac{\pi}{2}] \rightarrow R$ given by $g(x) = \cos x$,where $R$ is the set of real numbers. Consider the following statements:
Statement $(I)$: $f$ and $g$ are one-one.
Statement $(II)$: $f+g$ is one-one.
Which of the following is correct?

Let $f(x) = \cos(\sqrt{P}x),$ where $P = [\lambda]$ and $[.]$ denotes the Greatest Integer Function. If the period of $f(x)$ is $\pi$,then:

What is the nature of the function $f(x) = 2 |x - 1| + 3 |x - 2|$ in the interval $(1, 2)$?

Find the number of all onto functions from the set $\{1, 2, 3, \ldots, n\}$ to itself.