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 Prove that the Greatest Integer Function f : R → R, given by f(x) = [x], is neither
one-one nor onto, where [x] denotes the greatest integer less than or equal to x