Define F: Z -> Z by the rule
F(n) = 2 − 3n,
for each integer n.
(i)
Is F one-to-one?
Suppose
n1
and
n2
are any integers, such that
F(n1) = F(n2).
Substituting from the definition of F gives that
2 − 3n1 =
.
Solving this equation for
n1
and simplifying the result gives that
n1 =
.
Therefore, F is
---Select---
.
(ii)
Show that F is not onto.