Question

Consider functions f and g such that composite gof is defined and is one-one. Are f and g both necessarily one-one.​

Answer 1

Solution Consider f : {1, 2, 3, 4} → {1, 2, 3, 4, 5, 6} defined as f(x) = x, ∀ x and

g : {1, 2, 3, 4, 5, 6} → {1, 2, 3, 4, 5, 6} as g (x) = x, for x = 1, 2, 3, 4 and g (5) = g (6) = 5.Then, gof(x) = x ∀ x, which shows that gof is one-one. But g is clearly not one-one