Let $A$ be a set containing $10$ distinct elements. Then the total number of distinct functions from $A$ to $A$ is:

Let $f: \mathbb{Z} \rightarrow \mathbb{Z}$ be defined by $f(x) = x^3 + 2$. Then,$f$ is . . . . . . .

For real $x,$ let $f(x) = x^3 + 5x + 1,$ then

$f: N \rightarrow N, f(x) = x^3$ is . . . . . . .

$f(x) = x + \sqrt{x^2}$ is a function from $R \to R$,then $f(x)$ is

Let $f: R \rightarrow R$ be a function defined by
$f(x) = \begin{cases} x^2 \sin \left(\frac{\pi}{x^2}\right) & \text{if } x \neq 0 \\ 0 & \text{if } x = 0 \end{cases}$
Then which of the following statements is $TRUE$?