If the mapping f : {1, 3, 4} → {1, 2, 5} and g : {1, 2, 5} → {1, 3}, given by

f = {(1, 2), (3, 5), (4, 1)} and g = {(2, 3), (5, 1), (1, 3), write fog.

Formula:-

(i)Let f : AB and g : BC be two functions.

Then, the composition of f and g, denoted by g o f, is defined as the function g o f : AC

given by g o f (x) = g (f (x))

Given:-

(i)f : {1, 3, 4} → {1, 2, 5}

(ii)g : {1, 2, 5} → {1, 3}

(iii)f = {(1, 2), (3, 5), (4, 1)}

(iv)g = {(2, 3), (5, 1), (1, 3)

fog(1)=f(g(1))=f(3)=5

fog(2)=f(g(2))=f(3)=5

fog(5)=f(g(5))=f(1)=2

fog={(1,5)(2,5)(5,2)}