Show that the function f : R∗ → R∗ defined by f (x) =1/x is one-one and onto, where R∗ is the set of all non-zero real numbers. Is the result true, if the domain R∗ is replaced by N with co-domain being same as R∗?

Answer 

Show that the function f : R∗ → R∗ defined by f (x) =1/x is one-one and onto, where R∗ is the set of all non-zero real numbers. Is the result true, if the domain R∗ is replaced by N with co-domain being same as R∗?

 

 

 

 

 

 

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