Kyle C.

asked • 03/08/16

Prove that the function f : Z ? N defined by f(x)=(|4x+1|+1)/2 is injective

PLEASE HELP

1 Expert Answer

By:

Arnold F. answered • 03/08/16

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College Professor & Expert Tutor In Statistics and Calculus

Kyle C.

Thank you so much Arnold! S
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03/08/16

Kyle C.

So just to be sure this means its not injective right? Do I need to do all the cases if the first case proves its not injective?
 
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03/08/16

Arnold F.

I believe it is injective:
 
1. For case 1 above to be true:  4x+1=4y+1 so x=y (this is what we needed to show for injective to hold)
 
2. For case 2 the same
 
3. Cases 3 and 4 can't happen, that is the inside of the abs val can't be negative in one and positive in the other and still be equal (try it out.)
 
So the result is: if f(x)=f(y) then x=y.
 
 
Let me know if this makes sense to you.
 
 
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03/08/16

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