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

Which of the following is correct

Let $A=\{1,2,3,4,5\}$ and $B=\{1,2,3,4,5,6\}$. Then the number of functions $f: A \rightarrow B$ satisfying $f(1)+f(2)=f(4)-1$ is equal to

If $f(x) = \frac{x}{{x - 1}} = \frac{1}{y}$, then $f(y) = $

Let ${a_2},{a_3} \in R$ such that $\left| {{a_2} - {a_3}} \right| = 6$ and $f\left( x \right) = \left| {\begin{array}{*{20}{c}}
1&{{a_3}}&{{a_2}}\\
1&{{a_3}}&{2{a_2} - x}\\
1&{2{a_3} - x}&{{a_2}}
\end{array}} \right|,x \in R.$ Then the greatest value of $f(x)$ is

solve $\frac{{1 - \left| x \right|}}{{2 - \left| x \right|}} \ge 0$