If $f: R \rightarrow R$ is defined by $f(x) = \begin{cases} 2x & : x > 3 \\ x^2 & : 1 < x \leq 3 \\ 3x & : x \leq 1 \end{cases}$,then the value of $f(-1) + f(2) + f(4)$ is:

Let $A = R - \{3\}$ and $B = R - \{1\}$. Consider the function $f: A \rightarrow B$ defined by $f(x) = \left(\frac{x-2}{x-3}\right)$. Is $f$ one-one and onto? Justify your answer.

Let $f: R \rightarrow R$ be defined as $f(x)=x^{4}$. Choose the correct answer.

Show that a one-one function $f: \{1, 2, 3\} \rightarrow \{1, 2, 3\}$ must be onto.

Let $S = \{1, 2, 3, 4, 5, 6\}$. Then the number of one-one functions $f: S \rightarrow P(S)$,where $P(S)$ denotes the power set of $S$,such that $f(n) \subset f(m)$ whenever $n < m$ is $..................$

Show that the function $f: R \rightarrow R$ defined as $f(x) = x^{2}$ is neither one-one nor onto.