How to find the inverse of f?

Question

$ f : A \rightarrow B $ where $ A = B = \left \{4,5,6,7 \right \} $

$ f = \left \{ (4,6),(5,5),(6,7),(7,5) \right \} $

Find $ f^{-1} $

---

I know how to find the inverse of $ f $ if it were something like $ f(x) = 2x + 3 $ by finding $ f(y) = x $... How should I approach this problem?

Answer 1

$f : A \rightarrow B $, where

$\begin{cases} A = B = \{4,5,6,7 \} \\ f = \{ (4,6),(5,5),(6,7),(7,5)\} \end{cases}$

is a function $f\subset A\times B$, while $f^{-1}\subset B\times A$ is the relation $f^{-1} = \{ (6,4),(5,5),(7,6),(5,7)\}$ where all the $(x,y)$ is reversed to $(y,x)$. Since both $(5,5),(5,7)\in f^{-1}$ the relation $f^{-1}$ can't be a function.