Hence, f is not onto Example 8 Show that the function f : N → N, given by f(x) = 2x, is one-one but not
onto Solution The function f is one-one, for f (x1) = f(x2) ⇒ 2x1 = 2x2 ⇒ x1 = x2 Further,
f is not onto, as for 1 ∈ N, there does not exist any x in N such that f(x) = 2x = 1