4. Let f: N → N be defined by f(x) = (n+2, if n is odd n, if n is even state whether the function fis one-one, onto or bijective. Justify your answer.
Answers
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
Answer:
PI is an indicator of the relative strength of the pulsatile signal from pulse oximetry and has been found to be a reliable indicator of peripheral perfusion. PI is calculated by dividing the pulsatile signal (AC) by the nonpulsatile signal (DC) times 100, and is expressed as a percent ranging from 0.02% to 20%.PI is an indicator of the relative strength of the pulsatile signal from pulse oximetry and has been found to be a reliable indicator of peripheral perfusion. PI is calculated by dividing the pulsatile signal (AC) by the nonpulsatile signal (DC) times 100, and is expressed as a percent ranging from 0.02% to 20%.
Step-by-step explanation:
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