Question:
Mark (√) against the correct answer in the following:
If $f=\{(1,2),(3,5),(4,1)\}$ and $g=\{(2,3),(5,1),(1,3)\}$ then $(g \circ f)=?$
A. $\{(3,1),(1,3),(3,4)\}$
B. $\{(1,3),(3,1),(4,3)\}$
C. $\{(3,4),(4,3),(1,3)\}$
D. $\{(2,5),(5,2),(1,5)\}$
Solution:
$g=\{(2,3),(5,1),(1,3)\}$
$(g \circ f)=\{(\operatorname{dom}(f), 3),(\operatorname{dom}(f), 1),(\operatorname{dom}(f), 3)\}$
$\Rightarrow(g \circ f)=\{(1,3),(3,1),(4,3)\}$