Therefore f is not onto Example 12  Show that f : N → N, given by
1,if
is odd,
( )
1,if
is even
x
x
f x
x
x
+
=   
−
 
is both one-one and onto Fig 1 4
Rationalised 2023-24
MATHEMATICS
10
Solution  Suppose f (x1) = f (x2)