Question

F(n) = {n/2 if n is even 3n+1 if n is odd}

Answer 1

Answer:

f(n)={

2

n+1

,if n is odd

2

n

,if n is even

} for all n∈N

f:N→N is defined as

It can be observed that:

f(1)=

2

1+1

=1 and f(2)=

2

2

=1

∴f(1)=f(2), where 1



=2

∴f is not one-one.

Consider a natural number (n) in co-domain NCase I: n is odd

∴n=2r+1 for some r∈N.

Then, there exists 4r+1∈N such that f(4r+1)=

2

4r+1+1

=2r+1

Case II: n is even

∴n=2r for some r∈N.

Then, there exists 4r∈N such that f(4r)=

2

4r

=2r

∴f is onto.

Hence, f is not a bijective function

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