Question

Let \(f:\{1,3,4\}→\{1,2,5\}\) and g:{1,2,5}→{1,3} be given by f = {(1,2),(3,5),(4,1)} and g ={(1,3),(2,3),(5,1)}.Write down gof.

Answer 1

The functions f: {1, 3, 4} → {1, 2, 5} and g: {1, 2, 5} → {1, 3} are defined as f = {(1, 2), (3, 5), (4, 1)} and g = {(1, 3), (2, 3), (5, 1)}.

gof(1)=g(f(1))=g(2)=3 [f (1)=2 and g(2)=3]
gof(3)=g(f(3))=g(5)=1 [f (3)=5 and g(5)=1]
gof(4)=g(f(4))=g(1)=3 [f (4)=1 and g(1)=3]