If $f: S \rightarrow R$ where $S$ is the set of all non-singular matrices of order $2$ over $R$ and $f\left(\begin{bmatrix} a & b \\ c & d \end{bmatrix}\right) = ad - bc$, then:

Consider the following statements:
Statement-$I$ : $A$ function $f: A \rightarrow B$ is said to be one-one if and only if $f(x) \neq f(y) \Rightarrow x \neq y$.
Statement-$II$ : $A$ relation $f: A \rightarrow B$ is said to be a function if $x \neq y \Rightarrow f(x) \neq f(y)$.
Then which one of the following is true?

The function $f:[0,3] \rightarrow [1,29]$,defined by $f(x)=2x^3-15x^2+36x+1$,is

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

Let $A = \{x, y, z, u\}$ and $B = \{a, b\}$. $A$ function $f: A \rightarrow B$ is selected randomly. The probability that the function is an onto function is

Let $f:[0,1] \rightarrow [-1,1]$ and $g:[-1,1] \rightarrow [0,2]$ be two functions such that $g$ is injective and $g \circ f: [0,1] \rightarrow [0,2]$ is surjective. Then,