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∗∗∗∗∗ 2 Check the injectivity and surjectivity of the following functions:
(i) f : N → N given by f(x) = x2
(ii) f : Z → Z given by f(x) = x2
(iii) f : R → R given by f(x) = x2
(iv) f : N → N given by f(x) = x3
(v) f : Z → Z given by f(x) = x3
3