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

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

Let $R$ be the set of all real numbers and $f: R \rightarrow R$ be a continuous function. Suppose $|f(x) - f(y)| \geq |x - y|$ for all real numbers $x$ and $y$. Then,

The function $f: R \rightarrow R$ defined by $f(x)=\frac{x}{\sqrt{1+x^2}}$ is

Show that the function $f : R \rightarrow R$ given by $f(x) = x^{3}$ is injective.

Which of the following function$(s)$ is/are transcendental?