If $f : R \rightarrow R$ is defined as $f(x) = x - [x] + 3$,$\forall x \in R$,then $f$ is

If $f(x)=|x-1|+|x-2|+|x-3|$ for $2 < x < 3$,then $f$ is

Let $f : N \rightarrow N$ be defined by $f(n) = \begin{cases} \frac{n+1}{2}, & \text{if } n \text{ is odd} \\ \frac{n}{2}, & \text{if } n \text{ is even} \end{cases}$ for all $n \in N$. State whether the function $f$ is bijective. Justify your answer.

If $f: R \to R$ is a continuous function such that $|f(x) - f(y)| \geqslant |e^x - e^y|$ for all $x, y \in R$,then $f(x)$ is:

Define $f: R \rightarrow R$ by $f(x) = \max \{x+1, 1-x, 2\}$. Then,$f$ is

Let $R = \{ a, b, c, d, e \}$ and $S = \{1, 2, 3, 4\}$. The total number of onto functions $f: R \rightarrow S$ such that $f(a) \neq 1$ is equal to $.............$.