Check the injectivity and surjectivity of the following function f : R → R given by f(x) = x Square

Check the injectivity and surjectivity of the following functions: (i) f : N ->N given by f(x)=x^2 (ii) f : Z-> Z given by f(x)=x^2 (iii) f : R ->R given by f(x)=x^2 (iv) f : N-> N given by f(x)=x^3 (v) f : Z → Z given by f(x) = x^3

The function f:R to R given by f(x)=x^(2)+x is

Discuss the surjectivity of the following functions: f: R-> given by f(x)=x^3+2 for all x in Rdot

Check the nature of the following function. (i) f(x)=sin x, x in R " (ii) " f(x) =sin x, x in N

Function f : R rarr R , f(x) = x + |x| , is

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

The function f:R rarr R, f(x)=x^(2) is

Show that the function f: R->R given by f(x)=x^3+x is a bijection.

Prove that the function f : R ->R , given by f (x) = 2x , is one-one and onto.

Show that the function f: R ->R is given by f(x)=1+x^2 is not invertible.