Question

Let A = {1, 2, 3, 4} and f : A → A be given by f = {(1, 4), (2, 3), (3, 2), (4, 1)}. Then f^–1 = ___________.

Answer 1

Given: A function f : A → A be given by f = {(1, 4), (2, 3), (3, 2), (4, 1)}

$$\begin{gathered} f=\left\{\left(1,4\right),\left(2,3\right),\left(3,2\right),\left(4,1\right)\right\} \\ \Rightarrow f^{-1}=\left\{\left(4,1\right),\left(3,2\right),\left(2,3\right),\left(1,4\right)\right\} \\ \mathrm{Thus},f^{-1}=\left\{\left(4,1\right),\left(3,2\right),\left(2,3\right),\left(1,4\right)\right\} \end{gathered}$$

Hence, $f^{-1}=\underline{\left\{\left(4,1\right),\left(3,2\right),\left(2,3\right),\left(1,4\right)\right\}}.$