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

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

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

Show that the function f:NtoN defined by f(x)=2x-1 is one-one but not onto.

Show that the function f defined by f(x)=|1-x+x|, where x is any real number, is a continuous function.

Show f:R rarr R " defined by " f(x)=x^(2)+x " for all " x in R is many-one.

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

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