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

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)}.
it is clear that f(1) = 2, f(3) = 5, f(4) = 1
similarly, g(1) = 3, g(2) = 3 , g(5) = 1

now, gof(x)= g(f(x)), domain of gof = domain of f
so, gof(1) = g(f(1)) = g(2) = 3
gof(3) = g(f(3)) = g(5) = 1
gof(4) = g(f(4)) = g(1) = 3

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