Question

If f : {5, 6} $\to$ {2, 3} and g : {2, 3} $\to$ {5, 6} are given by f = {(5, 2), (6, 3)} and g = {(2, 5), (3, 6)}, then find fog. [NCERT EXEMPLAR]

Answer 1

We have,
f : {5, 6} $\to$ {2, 3} and g : {2, 3} $\to$ {5, 6} are given by f = {(5, 2), (6, 3)} and g = {(2, 5), (3, 6)}

As,
fog(2) = f(g(2)) = f(5) = 2,
fog(3) = f(g(3)) = f(6) = 3,

So,
fog : {2, 3} $\to$ {2, 3} is defined as
fog = {(2, 2), (3, 3)}