question_answer 17)

Show that the function defined by  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:

 Injectivity : Lee x1, x1 such that f(x1) = f(x2)              is one ? one.       Surjectivity : Let   be any element                    Corresponding to every element , there exists  such that f        is onto       However if the domain R* of f is replaced by N, then function f will remain one-one but not onto.       This is because for comain N, range of f(x) is