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

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

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.

Let R+ be the set of all non negative real numbers. Show that the function f: R_(+) to [4, infty] given by f(x) = x^2 + 4 is invertible and write inverse of 'f'.

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

Show that the function given by f (x) = e ^(2x) is increasing on R.

Show that the function f : Z to Z defined by f(x) = x^(3), AA x in Z is injective but not surjective.

Show that the function f : N to N defined by f(x) = x^(3), AA x in N is injective but not surjective.