Question

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 1

∴ 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.