Function form understanding

Question

I dont understand what is the function when im given this kind of form: f= {<1,1>,<2,3>,<3,2>}.

I understand functions when they are given in lambda form.

For example how can I find the function composition of f?

Answer 1

Here $f$ is a map defined on $\{1,2,3\}$ with range $\{1,2,3\}$ and is given by $f(1)=1$, $f(2)=3$, $f(3)=2$ (that is $f(x)=y$ if $\langle x,y\rangle$ appears in the set). Thus $f\circ f$ is the identity on $\{1,2,3\}$ because for example $f(f(2))=f(3)=2$. Thus $f\circ f=\{\langle 1,1\rangle, \langle 2,2\rangle, \langle 3,3\rangle\}$.