Let $A=\{1,2,3,4\}$. Let $f: A \rightarrow A$ and $g: A \rightarrow A$, defined by $f=\{(1,4),(2,1),(3,3),(4,2)\}$ and $g=\{(1,3),(2,1),(3,2),(4,4)\}$
Find (i) f of.

Solution:

(i) f of
We need to find: $f$ o $f$
Formula used: $f$ f $f=f(f(x))$
It is given that: $f=\{(1,4),(2,1),(3,3),(4,2)\}$
Solution: We have,
$\begin{array}{l}
\operatorname{fof}(1)=f(f(1))=f(4)=2 \\
\text { fof }(2)=f(f(2))=f(1)=4 \\
\text { fof }(3)=f(f(3))=f(3)=3 \\
\text { fof }(4)=f(f(4))=f(2)=1
\end{array}$
Ans) fo $f=\{(1,2),(2,4),(3,3),(4,1)\}$