Question

Let f:{1,3,4} $\to$ {1,2,5}and g:{1,2,5} $\to$ {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} $\to$ {1,2,5}and g:{1,2,5} $\to$ {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 $[\because f(1)=2$ and g(2)=3]
gof(3)=g(f(3))=g(5)=1 $[\because f(3)=5$ and g(5)=1]
gof(4)=g(f(4))=g(1)=3 $[\because f(4)=1$ and g(1)=3]

gof = {(1,3), (3,1), (4,3)}