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∗?
∴ g is one – one. Further, it is clear that g is not onto as for 1.2 ∈ R* there does not exit any x in N such that g(x)=1/1.2. Hence, function g is one-one but not onto.
