Consider the function $f ( n ) = 2 \lfloor n / 2 \rfloor$ from $\mathbf { Z }$ to $\mathbf { Z }$. Is this function one-to-one? Is this function onto? Justify your answers.

Name: Consider the function $f ( n ) = 2 \lfloor n / 2 \rfloor$ from $\mathbf { Z }$ to $\mathbf { Z }$. Is this function one-to-one? Is this function onto? Justify your answers.
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Question

Quizplus · Accepted Answer

The Answer is Note that

f ( 0 ) = 2 \lfloor 0 / 2 \rfloor = 0

and

f ( 1 ) = 2 \lfloor 1 / 2 \rfloor = 0

. Hence

f

is not one-to-one. Note that

f ( n )

is even for every integer

n

. Hence

f

is not onto.

Consider the Function f(n)=2⌊n/2⌋f ( n ) = 2 \lfloor n / 2 \rfloorf(n)=2⌊n/2⌋

Consider the Function $f ( n ) = 2 \lfloor n / 2 \rfloor$