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 Question from nayeem, a parent: I tried with many functions but I am not getting the exact values please help me A give an example of a function whose domain equals the set of real numbers and whose range equals the set the set {-1,0,1}? B Give an example of a function whose domain equals (0,1)and whose range equals [0,1] C. Give n example of a function whose is the set of positive integers and whose range is the set of positive even integers D. Give an example of a function whose domain is the set of positive even integers and whoce range is the set of positive odd integers E give an example of function whose domain is the set of integers and whoce range is the set of positive integers. F. Give an example of function whose domain is the set of positive integers and whoce range is the set of integers. plese show me the work Please give me the trick of finding such functions

Nayeem,

I'm going to give you the trick and let you try to apply it.

And I'm certainly not going to show you the work!

Trick: don't assume that the functions have every "nice" property you know of. They may be non-continuous, or not 1-1. For instance, the function $x -> x^2$ maps the open interval (-1,1) onto the half-open interval [0,1), but it gets away with this by not being 1-1.

God Hunting!
RD

A second trick is that you might need to express the function in a piecewise fashion.

Harley

Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.