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.

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

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 f : R^+toR^+ defined by f (x) =x+1/x is injective, but not surjective .

Show that the function f: Z->Z defined by f(x)=x^2 for all x in Z , is a function but not bijective function.

Find whether the function f: Z rarr Z , defined by f(x) = x^(2) +5, AA x in Z is one-one or not.

Show that the function f:Z rarr Z defined by f(x)=x^(2)+x for all x in Z, is a many-one function.

Show that the function f:Z rarr Z defined by f(x)=x^(2)+x for all x in Z, is a many one function.

Consider the function f:NtoN , given by f(x)=x^3 . Show that the function ' f ' is injective but not surjective.

Show that the function f: ZvecZ defined by f(x)=x^2+x for all x in Z , is a many one function.