Show that the function `f: R toR.`
defined as `f (x) =x ^(2),` is neither one-one nor onto.

Show that the Modulus function f : R to R given by f (x) = [x] is neither one-one nor onto.

Show that the function f: R to R given by f (x) = x ^(3) is injective.

Show that the Modulus Functions f : R to R, given by f (x) =|x|, is neither one-one nor onto, whre |x| is x, if x is positive or 0 and |x| is -x, if x is negative.

Show that the function f : R to R defined by f(x) = x^(2) AA x in R is neither injective nor subjective.

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

Show that the function f : R to R , defined by f(x) = 1/x is one-one and onto, where R, is the set of all non-zero real numbers.

Show that the function f: R_(**)to R _(**) defined by f (x) = 1/x is one-one and onto, where R _(**) is the set of all non-zero numbes. Is the result true, if the domain R _(**) is replaced by N with co-domain being same as R_(**) ?

If f : R to R defined by f(x) = 1+x^(2), then show that f is neither 1-1 nor onto.

Show that the function f : N to N defined by f(x) = x^(2), AA x in N is injective but not surjective.