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