Fig 1 3
Example 10  Show that the function f : N → N, given by f (1) = f (2) = 1 and f(x) = x – 1,
for every x > 2, is onto but not one-one Solution  f is not one-one, as f (1) = f (2) = 1 But f is onto, as given any y ∈ N, y ≠ 1,
we can choose x as y + 1 such that f (y + 1) = y + 1 – 1 = y