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:

Let $f : R \rightarrow R$ be a function such that $f(x) = \frac{x^2+2x+1}{x^2+1}$. Then

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

Let $f(x) = \begin{cases} x \sin \left(\frac{1}{x}\right) & \text{when } x \neq 0 \\ 1 & \text{when } x = 0 \end{cases}$ and $A = \{x \in \mathbb{R} : f(x) = 1\}$. Then,$A$ has

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

If $n(A) = 5$ and $n(B) = 8$,how many possible functions can be defined from $A$ to $B$?