Let $A = \{1, 2, 3, 4\}$ and $R : A \to A$ be the relation defined by $R = \{ (1, 1), (2, 3), (3, 4), (4, 2) \}$. The correct statement is

Let $f: R \rightarrow R$ be defined by $f(x) = \left\{\begin{array}{cc} 2x, & x > 3 \\ x^2, & 1 < x \leq 3 \\ 3x, & x \leq 1 \end{array}\right.$. Then,the value of $f(-2) + f(3) + f(4)$ is:

Let a function $f: (0, \infty) \to (0, \infty)$ be defined by $f(x) = |1 - \frac{1}{x}|$. Then $f$ is

For $0 \leq x \leq 1$,what type of function is $f(x) = |x| + |x - 1|$?

Let $R$ be the set of real numbers and $f: R \rightarrow R$ be defined by $f(x) = \frac{\{x\}}{1+[x]^2}$,where $[x]$ is the greatest integer less than or equal to $x$,and $\{x\} = x-[x]$. Which of the following statements are true?
$I.$ The range of $f$ is a closed interval.
$II.$ $f$ is continuous on $R$.
$III.$ $f$ is one-one on $R$.

Let $A=\{1,2,3\}, \,B=\{4,5,6,7\}$ and let $f=\{(1,4),\,(2,5),\,(3,6)\}$ be a function from $A$ to $B$. Show that $f$ is one-one.