Find a function whose domain is the set of all integers and whose target is the set of all positive integers that satisfies each set of properties.
Find a function whose domain is the set of all integers and whose target is the set of all positive integers that satisfies each set of properties.
Step:-1
Set of integers = ,
set of positive integers=
Note:- 0 is not included in set of all positive integers.
Part (b):- One-to-one but not onto.
Let f be a function such that
This is one-to-one function because
but not onto because there is no such that f(n)=2, 8, 14,.... that is, 2, 8, 14,... do not have a pre-image.
Step:-2
Part (c):- onto but not one-to-one.
Let f be a function such that
+1
This is not one-to-one function because
as
and so on.
but onto because every positive integer in have a pre-image in .
Step:-3
Part (d):- one-to-one and onto.
Let f be a function such that
This is one-to-one function because
and it is onto because every positive integer in have a pre-image in .
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