This implies that 51 in N is not roll number of any student of
the class, so that 51 can not be image of any element of X under f 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