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.

Show that the function f: ZvecZ 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.

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: R->R defined by f(x)=3x^3+5 for all x in R is a bijection.

Show that the function f: RvecR defined by f(x)=3x^3+5 for all x in R is a bijection.

Show that the function f:R rarr R defined by f(x)=3x^(3)+5 for all x in R is a bijection.

Show that the function f:R rarr R defined by f(x)=3x^(3)+5 for all x in R is a bijection.

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

If ZZ be the set of integers, prove that the function f: ZZ rarrZZ defined by f(x)=|x| , for all x in Z is a many -one function.

Show that the function defined by f(x)=cos(x^2) is a continuous function.